Question Type 2: Solving separable differential equations Bootcamps

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

Solve the differential equation $\frac{dy}{dx}=\frac{y}{1+x^2}$, given $y(0)=3$.

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

Solve the differential equation $\frac{dy}{dx}=(4x+1)y^2$ (general solution).

Solve the differential equation $\frac{dy}{dx}=(4x+1)y^2$, given $y(0)=1$.

Solve the differential equation $\frac{dy}{dx}=y^2\sin x$, given $y\bigl(\tfrac{\pi}{2}\bigr)=1$.

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

Solve the differential equation $\frac{dy}{dx}=\frac{x e^{-x}}{y}$, given $y(0)=2$.

Solve the differential equation $\frac{dy}{dx}=\frac{5x^4-2x}{y^3}$.

Solve the differential equation $\frac{dy}{dx}=x^2e^x\,y$, given $y(0)=1$.

Solve the differential equation $\frac{dy}{dx}=\frac{y+1}{x}$, given $y(1)=0$.

Solve the differential equation $\frac{dy}{dx}=\frac{2x+3}{3y^2-1}$, given $y(0)=0$.