IB Mathematics Applications & Interpretation Question Type 4: Finding the Particular Solution for a Separable Differential Equation Using the General Solution Exercises

Solve the differential equation $$\frac{dy}{dx}=-4y$$ with the initial condition $y(1)=5$ to find the particular solution.

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

Find the particular solution to the separable equation $$\frac{\text{d}y}{\text{d}x}=2x{y}^2$$ given $y(0)=1$.

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

Find the particular solution of the separable differential equation $$\frac{dy}{dx}=3y$$ satisfying $y(0)=2$.

Solve the initial-value problem $\frac{\text{d}y}{\text{d}x}=\frac{y^2}{x^2}$, given that $y(1)=2$, to find the particular solution.

Solve the initial-value problem

$$\frac{dy}{dx}=\frac{x+1}{y},y(0)=3$$

to find the particular solution.

Solve the differential equation $\frac{dy}{dx}=\frac{y}{x}$ with initial condition $y(1)=3$ to find the particular solution.

Determine the particular solution of the differential equation $\frac{dy}{dx}=y^2{e}^x$, given that $y=1$ when $x=0$.

Determine the particular solution of $\frac{dy}{dx}=y^2\sin x$ with the condition $y\left(\frac{\pi }{2}\right)=2$.

Find the particular solution of the differential equation $\frac{\text{d}y}{\text{d}x}=x{y}^3$, given that $y=1$ when $x=1$.