Practice — Differential Equations

Easy

Find the general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \).

Easy

Solve the differential equation \( \frac{dy}{dx} + y = 0 \).

Easy

The differential equation \( \frac{dy}{dx} = \frac{y}{x} \) represents which type of equation?

Medium

Solve \( \frac{dy}{dx} = \frac{x + y}{x} \) given \( y(1) = 0 \).

Medium

Find the particular solution of \( \frac{dy}{dx} = 2xy^2 \) with \( y(0) = 1 \).

Hard

Solve the exact differential equation \( (2xy + y^2)dx + (x^2 + 2xy)dy = 0 \).

Hard

Find the solution of the Bernoulli equation \( x \frac{dy}{dx} + y = x y^2 \).

Medium

Given the differential equation \( \frac{dy}{dx} = \frac{x + 2y}{2x - y} \), find the type of equation.

Hard

Solve the differential equation \( (y + x e^{xy}) dx + (x + y e^{xy}) dy = 0 \).

Differential Equations