UW MATH 207: Introduction to Differential Equations

MATH 207 (formerly numbered MATH 307) is UW's introductory ordinary differential equations course: first- and second-order equations, solution techniques, and the Laplace transform, with applications to physical systems. As of autumn 2021, students may use either the 207 or 307 number toward degree requirements.

Fennie is independent and not affiliated with University of Washington. This is an unofficial study guide.

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What makes it hard

ODEs are a toolbox course — each equation type has its own method, and recognizing which technique a problem wants is the real challenge under exam time. Second-order equations and the Laplace transform are the difficulty spikes, and the algebra is heavy enough that small slips cascade. Students who memorize procedures without understanding when they apply get stuck the moment a problem looks unfamiliar.

What you'll cover

• First-order differential equations
• Separable and linear equations
• Second-order linear equations
• Method of undetermined coefficients
• The Laplace transform
• Applications to physical systems

The MATH 207 study guide

How to study for UW MATH 207, step by step.

1
Build a method-recognition chart early
MATH 207 is really a collection of techniques — separable, linear, exact, undetermined coefficients. Make a one-page decision chart mapping equation form to method, because the exam challenge is choosing the right tool, not executing it.
2
Mix problem types in every practice session
Don't drill one technique at a time — shuffle them, so each problem starts with the recognition step. That mirrors exactly how exams present a bare equation with no label.
3
Give the Laplace transform its own study block
The Laplace material feels like a separate course and is a reliable difficulty spike. Work through the transform table and inverse-transform problems until the mechanics are automatic.
4
Keep the algebra clean
Most lost points in ODEs are algebra slips, not conceptual errors. Slow down on the manipulation, and check each solution by substituting it back into the original equation.
5
Hand the technique drilling to Fennie
Upload your MATH 207 syllabus and Fennie's Daily Plan interleaves the solution techniques across the quarter, paced to your exam dates, with practice quizzes on method-recognition generated from your actual course materials. Free to start.
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How Fennie helps with MATH 207

Fennie's Daily Plans interleave MATH 207's solution techniques across the quarter so you build the recognition exams demand, and pace everything to your midterm dates. Chat through which method a given equation wants or why a Laplace inverse works, and generate practice problems mixing technique types to simulate exam conditions.

FAQ

Is MATH 207 the same as MATH 307?

Yes — as of autumn 2021, UW renumbered MATH 307 to MATH 207, and you can apply either number toward degree requirements. The content (introductory ODEs) is the same.

Is MATH 207 hard?

It's moderate but technique-heavy. The difficulty is recognizing which solution method a problem wants and keeping the algebra clean. Second-order equations and the Laplace transform are the usual difficulty spikes.

What should I review before MATH 207?

Integration techniques from the calculus sequence, since solving ODEs leans heavily on them, plus solid algebra. Most lost points are integration or algebra slips, not conceptual errors.

Pass MATH 207 with a plan, not a cram

Upload your MATH 207 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.

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