Differential Equations (Standard)

Multi-step exam-style items.

Phase 2 · AP Calculus

Differential Equations: core idea

Separate and integrate.

Solve $y'=2y$ , $y(0)=3$ . Find $y(1)$ .

Hint: Separate. Answer: 3e^2.

1. Solve $y'=x/y$ with $y(0)=2$ . Find $y(\sqrt3)^2$ .
2. Solve $y'+y=0$ , $y(0)=5$ . Find $y(\ln2)$ .
3. Model $P'=0.1P$ , $P(0)=100$ . Find $P(10)$ .
4. Euler: $y'=y$ , $y(0)=1$ , step $h=0.5$ , one step: approx $y(0.5)$ ?
5. Separate $y'=xy$ , $y(0)=1$ . Find $y(2)$ .
6. Logistic $y'=y(4-y)$ : carrying capacity?
7. Solve $y'=e^{-x}$ , $y(0)=0$ . Find $y(\ln2)$ .
8. If $y''=y$ and $y=e^x$ , concavity at $0$ equals $y(0)$ ? Enter $y''(0)$ .
9. Particular solution $y'=2x$ with $y(1)=4$ : $y(0)$ ?