Part of the expanding PassProfessor catalog: This program is in the works — a chapter-simulation program covering the full scope of a differential equations course, organized chapter by chapter. Join the notify list and we will email you the day it launches.
This program is part of the expanding PassProfessor catalog — join the notify list and we’ll email you when enrollment opens.
PassProfessor’s Differential Equations program is a chapter-simulation program for students taking a differential equations course. You pick the course, then pick the textbook and edition your class uses, and the program builds chapter-based simulation exams optimized for that book’s chapter order — so the practice you do this week matches the chapter your instructor is teaching this week. The program is organized across 13 chapters plus in-depth practice sets, an applied modeling set, and an integrative synthesis set, covering first-order equations and modeling, separable and linear equations, exact equations in outline, second-order linear equations, undetermined coefficients and variation of parameters, applications in outline, systems of first-order linear equations, series solutions in outline, Laplace transforms, and numerical methods in outline. There is no licensing exam at the end of a differential equations course — there is your instructor’s exam, chapter by chapter — and this program is built to rehearse exactly that.
PassProfessor’s Differential Equations program is a chapter-simulation program for the undergraduate differential equations course: original practice organized chapter by chapter — first-order equations, second-order linear equations, systems of equations, Laplace transforms, and series and numerical methods in outline — matched by textbook and edition so chapter drills and timed simulation exams follow the chapter your instructor is teaching. It rehearses your instructor’s chapter tests and finals — there is no licensing exam for a college course — with results reported by chapter.
What this program is — and what it is not
It is a simulation of your course, not a licensing product. Licensing-exam prep rehearses one fixed, official exam. A college course works differently: your instructor chooses the textbook, sets the chapter order, and writes the exams. This program is designed around that reality. The textbook-and-edition selector aligns the simulations to the chapter sequence of the book your course actually uses, and chapter drills let you practice one chapter at a time, at the point in the semester when you need it.
It is not published, sponsored, or endorsed by any textbook publisher or author. PassProfessor is an independent study provider. The program is never branded or titled under a textbook’s name, and nothing in it reproduces textbook text, textbook figures, or a publisher’s test bank. Selecting your textbook only tells the program which chapter order to organize your practice around.
Every question is original. The bank was built from the published structure of a differential equations course — the standard chapter sequence and topic scope the discipline itself uses — and every stem, scenario, and answer option was written from scratch and checked against verified disciplinary facts. Sources supplied facts and course structure only; the questions are ours.
What’s included
Practice organized the way your course is organized. The bank follows a 13-chapter structure that mirrors the standard differential equations course, from introduction to differential equations, modeling, and direction fields through numerical methods, in outline, plus in-depth practice sets, an applied modeling set, and an integrative synthesis set. The full chapter-by-chapter breakdown is in the coverage table below.
Chapter drills. Practice a single chapter — only that chapter — until the misses stop repeating. Finished the Laplace lectures? Drill that chapter until the transform table feels automatic. Second-order test in ten days? Work the constant-coefficient chapter in sequence, the way your course presents it.
Chapter-based simulation exams. When a chapter test or a unit exam approaches, sit a timed simulation built from the chapters it covers, in the proportions your selected textbook’s organization suggests. Simulations draw questions you have not seen first, so a second or third run at the same chapter is a fresh test, not a memory exercise.
A textbook-and-edition selector. Different textbooks divide the same material into chapters differently — one book’s single chapter is another book’s two. When you select the textbook and edition your course uses, the program maps its bank onto that book’s chapter organization, so the chapter number in your practice means the same chapter in your syllabus.
Results broken down by chapter and topic. Your practice results report by chapter, so a weak area — say, variation of parameters, or Laplace transforms — shows up in your data while there is still time to fix it, not for the first time on a graded exam.
A note on editions and course versions. Instructors adopt different textbooks and different editions of the same textbook, and departments periodically revise the course itself. The bank’s organization follows the discipline’s standard chapter structure — the sequence the field itself teaches — and the selector maps that structure onto your edition’s numbering, so a chapter that your book splits in two, or merges into one, still lines up with the practice built for it. Where an instructor reorders chapters, chapter drills can be assembled in your course’s order; the practice follows the syllabus, not the other way around.
The course at a glance
Differential Equations has no single official exam, so there is no official exam-facts table to publish — your instructor’s syllabus is the authority for your course’s test dates, formats, and grading. What is standard is the scope of the discipline itself, summarized here as course background. For the full picture of what a differential equations course covers and how to study it, see our Differential Equations study guide.
| Undergraduate differential equations — the course this program simulates | |
|---|---|
| Course type | Undergraduate college course (a core course for engineering, physics, and mathematics programs; normally taken after the calculus sequence and often alongside or after linear algebra — prerequisites vary by institution) |
| Standard scope | Introduction to differential equations — classification, solutions, initial value problems, direction fields, and modeling; first-order equations — separable and linear equations, integrating factors, exact equations and substitution methods in outline; applications of first-order equations in outline; second-order linear equations — homogeneous equations with constant coefficients, characteristic equations, and reduction of order in outline; nonhomogeneous equations — undetermined coefficients and variation of parameters; applications — spring-mass motion and circuits in outline; higher-order linear equations in outline; systems of first-order linear equations — matrix form, eigenvalues, and the phase plane in outline; series solutions in outline; the Laplace transform — definition, properties, inverse transforms, and solving initial value problems, with step functions and impulses in outline; numerical methods in outline |
| How the course is assessed | Instructor-set chapter tests, unit exams, and a final — formats and weights vary by instructor and institution |
| This program’s bank | Chapter-based practice across 13 chapters + in-depth, applied, and synthesis sets |
| Program format | Chapter drills and chapter-based simulation exams, organized by your selected textbook/edition |
How the practice maps to the course
The program follows the standard chapter organization of the course, below. Chapter drills draw only from the chapter you select, and simulation exams can be built over any set of chapters.
| Chapter | Coverage |
|---|---|
| Introduction: Classification, Solutions, and Direction Fields | — |
| Modeling with First-Order Equations | — |
| Separable and Linear First-Order Equations | — |
| Exact Equations and Substitution Methods in Outline | — |
| Second-Order Linear Equations: Homogeneous Theory | — |
| Nonhomogeneous Equations: Undetermined Coefficients | — |
| Variation of Parameters and Reduction of Order in Outline | — |
| Applications: Motion, Vibration, and Circuits in Outline | — |
| Higher-Order Linear Equations in Outline | — |
| Systems of First-Order Linear Equations | — |
| Series Solutions in Outline | — |
| The Laplace Transform | — |
| Numerical Methods in Outline | — |
The outline chapters deserve a note: exact equations, variation of parameters at depth, series solutions, and numerical methods are introduced at orientation depth in many first courses and developed in later ones, and some courses place Laplace transforms before systems. The program’s textbook selector maps practice onto your book’s organization, so your drills carry the chapters — and the weights — your course actually assigns.
How to use it
- Join the notify list today. When the program opens, set up your course first: select Differential Equations, then select the textbook and edition your syllabus names.
- Drill the chapter you are in. After each lecture block, drill that chapter while the material is current. Short, chapter-matched practice beats a single long session the night before the test.
- Watch your chapter breakdown. Your results show which chapters are costing you. Return to the weakest chapter’s drill before moving on — differential equations is a methods course built in layers — first-order recognition trains the eye, second-order theory introduces the characteristic equation, and systems and Laplace methods restate both in new languages, so a weak method returns wearing later clothes.
- Simulate before each graded test. In the days before a chapter test or unit exam, sit a timed simulation over exactly the chapters it covers. Practice the pacing and the question style, not just the facts.
- Use the integrated set before midterms and finals. The cross-chapter questions combine chapters the way cumulative exams do. They are the closest rehearsal for a final that reaches back to the start of the term.
Frequently asked questions
Is this a licensing exam prep program? No. Differential equations is a college course, not a licensed credential, and there is no official differential equations exam at the end of it. This is a chapter-simulation program: it rehearses the tests your own instructor gives, chapter by chapter, using original practice built to the standard scope of the undergraduate course.
Which textbook does the program follow? The program is organized around the standard chapter structure of the differential equations course, and the textbook-and-edition selector maps practice onto your book’s chapter order when you set up your course. No textbook is named, branded, or reproduced — the selector only aligns chapter numbering.
Do I need linear algebra for this course? It depends on your institution and on the systems chapter. Many courses teach the eigenvalue steps they need as procedures; others assume a linear algebra prerequisite or co-requisite. Your catalog states the rule, and the program’s systems drills follow the standard course’s own presentation.
Does the program cover Laplace transforms? Yes — the transform is a full chapter in the standard course and in this program: the table, inverse transforms, derivatives, initial value problems, and step functions in outline. Courses that place it earlier are handled by the textbook selector’s chapter mapping.
Can I practice just one chapter? Yes — that is the core of the design. Chapter drills draw only from the chapter you select, and simulation exams can be built over any set of chapters, so your practice can match a single chapter test, a unit exam, or a cumulative final.
My course spends little time on series solutions. Will the practice still line up? Yes. Series solutions and numerical methods are outline chapters in the program, matching their usual weight in a first course. The textbook selector maps practice onto your book’s organization, and drills can be weighted by the chapters your course emphasizes.
Where do students usually need the most practice? Results in this course typically point to method recognition across mixed first-order types, the modification rule in undetermined coefficients, and the partial-fraction work inside Laplace problems. Chapter-level results in the program show which of these is costing you.
Is this the same as a calculus program? No. Calculus builds the derivatives and integrals this course uses; differential equations asks the reverse question — given a relation involving derivatives, find the function. They are separate courses with separate PassProfessor programs.
Does the program include modeling and applications? Yes, at the course’s own depth: first-order modeling is a taught chapter, and motion, vibration, and circuit applications appear in outline, as most first courses present them. The emphasis throughout is the standard course’s balance of method and model.
When can I start using the Differential Equations program? The program is in the works. Join the notify list on this page and we will email you the day it opens.
Disclaimer
PassProfessor is an independent exam-preparation and study provider, based in Salt Lake City, UT and operating entirely online. This program is study preparation only: it is not affiliated with, endorsed by, or sponsored by any textbook publisher, textbook author, college, university, or instructor, and it reproduces no textbook content. Practice questions are original, written to the published structure and standard scope of a differential equations course; they are not questions from any instructor’s exam or any publisher’s test bank. Your course syllabus is the authority for your course’s schedule, formats, and grading.