QUESTION 1 / 20 · BASICSEasy
What is the order of y″ + 3y′ − y = 0?
EULER'S METHOD
Step forward one slope at a time
When an equation can't be solved by hand, computers step along it: read the slope, walk a little way, repeat. Bigger steps are faster but drift from the true curve. Pick a model and change the step size.
exact solutionEuler steps
EXPONENTIAL GROWTHdy/dt = 0.8y, y(0) = 1Growth proportional to size. Euler always undershoots here, because the slope keeps rising during each step.
14.76Euler's estimate at the end
24.53exact value
What this differential equations test covers, in short
Twenty multiple-choice questions on ordinary differential equations at first- to second-year university level, four on each of five topics: basics, first-order methods, second-order linear equations, modelling, and numerical methods.
You'll need comfortable calculus; try the calculus test first if you're rusty. The test is our own and not normed.
By What's Your IQ · Reviewed 5 Oct 2026- Format
- 20 multiple-choice questions
- Level
- First- to second-year university
- Bonus
- Euler's method explorer, 3 models
- Scope
- Ordinary (not partial) differential equations