Practice — Differential Equations

Easy

What is the order of the differential equation \( \frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 0 \)?

Easy

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

Medium

Which of the following is a homogeneous differential equation?

Easy

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

Easy

The differential equation \( \frac{dy}{dx} + P(x)y = Q(x) \) is called:

Medium

Find the particular solution of \( \frac{dy}{dx} = y \tan x \), given \( y(\pi/4) = 2 \).

Medium

Which method is suitable to solve \( (2xy + y^2)dx + (x^2 + 2xy)dy = 0 \)?

Hard

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

Medium

If \( y = e^{mx} \) is a solution of \( \frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 0 \), find \( m \).

Hard

Given \( \frac{dy}{dx} = \frac{y}{x} + e^{x/y} \), which substitution is most appropriate?

Differential Equations