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 $\frac{\text{d}y}{\text{d}x} = 2xy^2$ 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

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

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 $\frac{\text{d}y}{\text{d}x} = xy^3$, given that $y = 1$ when $x = 1$.