Question Type 2: Separating a differential equation into two variables Exercises

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

Find the particular solution of $\frac{dy}{dx} = \frac{x}{y}$ satisfying $y(0)=3$.

Solve the differential equation $\frac{dy}{dx} = \frac{2x}{3y^{2}}$.

Solve the differential equation $\frac{dy}{dx} = y\,e^{x}$.

Find the particular solution of $\frac{dy}{dx} = y\,e^{x}$ satisfying $y(0)=3$.

Solve the differential equation $\frac{dy}{dx} = y^{2}\sin x$.

Solve the differential equation $\frac{dy}{dx} = (x^{2} + 1)\,y$.

Solve the differential equation $\frac{dy}{dx} = \frac{3x^{2}}{y+1}$.

Find the particular solution of $\frac{dy}{dx} = \frac{2x}{3y^{2}}$ satisfying $y(1)=2$.

Find the particular solution of $\frac{dy}{dx} = (x^{2}+1)\,y$ satisfying $y(0)=3$.

Find the particular solution of $\frac{dy}{dx} = \frac{3x^{2}}{y+1}$ satisfying $y(0)=0$.

Find the particular solution of $\frac{dy}{dx} = y^{2}\sin x$ satisfying $y(0)=3$.