Question Type 4: Finding the particular solution for a separable differential equation using the general solution Exercises

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

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

Solve the initial‐value problem $\frac{dy}{dx}=\frac{x+1}{y},\quad y(0)=3$ to find the particular solution.

Find the particular solution to the separable equation $\frac{dy}{dx}=2xy^2$ given $y(0)=1$.

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

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

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

Solve $\frac{dy}{dx}=\frac{y}{x}$ with $y(1)=3$ and find the particular solution.

Determine the particular solution of $\frac{dy}{dx}=y^2e^x$ given $y(0)=1$.

Solve the initial‐value problem $\frac{dy}{dx}=\frac{y^2}{x^2},\quad y(1)=2$ to find the particular solution.

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