IB Mathematics Applications & Interpretation Question Type 2: Separating a Differential Equation Into Two Variables Exercises

Find the particular solution of $\frac{\text{d}y}{\text{d}x}=\frac{3x^2}{y+1}$ satisfying the initial condition $y(0)=0$.

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

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

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

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

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

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

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

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

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

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

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