Account Sign in Sign up

← All lessons

Differential Equations (Foundations)

Core skills for this exam family.

Phase 2 · AP Calculus

Foundations Standard Advanced

Differential Equations: core idea

\frac{dy}{dx}=ky \Rightarrow y=Ce^{kx}

.

Example problem: hint and answer

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

Hint: Integrate. Answer: 9.

Practice (9 problems — type your answers)

1. Solve $y'=3$ , $y(0)=1$ . Find $y(4)$ .
2. If $y'=y$ and $y(0)=2$ , find $y'(0)$ .
3. Slope field $y'=x+y$ at $(0,1)$ : slope?
4. Equilibrium of $y'=y(1-y)$ : larger one?
5. Solve $y'=\cos x$ , $y(0)=0$ . Find $y(\pi/2)$ .
6. If $y'=x^2$ , find $y'(2)$ .
7. Solve $y'=0$ , $y(0)=5$ . Find $y(10)$ .
8. Direction of $y'=x-y$ at $(1,0)$ : slope?
9. If $y'=1/x$ for $x>0$ , $y(1)=0$ , find $y(e)$ .

Differential Equations Practice Problems — Foundations