UCLA MATH 33B: Differential Equations

MATH 33B is UCLA's ordinary differential equations course: first-order equations, second-order linear equations, the method of undetermined coefficients and variation of parameters, and applications to physical systems. It follows the 31 sequence and is required across engineering and the physical sciences.

Fennie is independent and not affiliated with UCLA. This is an unofficial study guide.

Build my MATH 33B study plan

What makes it hard

33B is method-heavy — each equation type has its own solution recipe, and the difficulty is recognizing which method applies and executing it cleanly under time pressure. The ten-week pace stacks the techniques quickly, and integration rust from earlier courses turns ODE problems into calculus problems at the worst moment.

What you'll cover

• First-order differential equations
• Separable and linear equations
• Second-order linear equations
• Undetermined coefficients and variation of parameters
• Applications and modeling
• Systems of differential equations

The MATH 33B study guide

How to study for UCLA MATH 33B, step by step.

1
Re-sharpen integration before the quarter
Every ODE method ends in an integral, and rusty integration turns 33B into a calculus course. Refresh integration by parts, partial fractions, and substitution in week one so technique never blocks the actual ODE work.
2
Build a method-selection flowchart
The core skill is recognizing the equation type and picking the matching method fast. Write an ordered checklist — separable, linear, exact, then second-order cases — and drill classifying equations until selection is instant.
3
Drill each method to a fixed routine
Undetermined coefficients and variation of parameters reward doing the setup identically every time. Rep each until the procedure is automatic and exam time goes to recognizing the type, not recalling the steps.
4
Connect 33A when systems arrive
Systems of ODEs are an eigenvalue exercise in disguise. If you've taken 33A, review eigentheory right before that unit; if not, give the linear-algebra mechanics extra attention.
5
Pace the methods with Fennie
Upload the MATH 33B syllabus and Fennie's Daily Plans schedule daily method practice toward the quarter's exams, generating classify-and-solve quizzes from your actual course materials. Free to start.
Start my MATH 33B plan free

How Fennie helps with MATH 33B

Fennie's Daily Plans pace MATH 33B's stack of solution methods across the ten-week quarter so each technique gets practiced before the next arrives. Chat through which method an equation calls for and why, and drill generated classify-and-solve quizzes until recognizing the equation type — the real exam skill — is automatic.

FAQ

Is MATH 33B hard at UCLA?

It's method-heavy more than deep — the challenge is recognizing equation types and executing the matching technique cleanly under quarter-pace time pressure. Students with solid integration skills find it manageable; rusty integration makes every problem harder than it should be.

What should I review before MATH 33B?

Integration techniques above all — parts, partial fractions, substitution — since every method culminates in an integral. If you're taking it after 33A, keeping eigenvalues fresh helps with the systems-of-equations unit at the end.

How do I study for MATH 33B exams?

Build a method-selection flowchart and drill classifying equations until you recognize the type instantly, then practice each solution method to a fixed routine. The exams reward fast correct method selection more than any single hard computation.

Pass MATH 33B with a plan, not a cram

Upload your MATH 33B materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.

Get started free

More UCLA courses

MATH 31A — Differential and Integral Calculus

MATH 31A is UCLA's first calculus course — limits, derivatives, optimization, and the basics of integration — required across engineering, physical science, economics, and life-science-adjacent tracks. Most STEM freshmen take it (or skip it via AP credit) in fall quarter.

MATH 31B — Integration and Infinite Series

MATH 31B covers integration techniques, applications, improper integrals, and infinite sequences and series including Taylor series. It's the second course in UCLA's main calculus sequence and a prerequisite for the multivariable courses that follow.

MATH 32A — Calculus of Several Variables

MATH 32A introduces multivariable calculus: vectors, vector-valued functions, partial derivatives, gradients, and optimization in several variables. It's required for engineering, physics, math, and CS-adjacent tracks, typically taken in the first year after the 31 sequence.

MATH 32B — Calculus of Several Variables

MATH 32B completes UCLA's multivariable calculus sequence: multiple integrals, change of variables, line and surface integrals, and the vector-calculus theorems of Green, Stokes, and Gauss. It follows 32A and is required across engineering and the physical sciences.