Question Type 3: Solving a separable differential equation to obtain the general solution Exercises

Find the general solution of the differential equation $\displaystyle\frac{dy}{dx}=\frac{2x}{y^2}$.

Find the general solution for $y$ in terms of $x$ for the differential equation $\frac{dy}{dx} = e^x y^2$.

Solve the logistic-type separable equation $\frac{dy}{dx}=y(1-y)$ to obtain the general solution.

Find the general solution of the differential equation $\frac{dy}{dx} = x e^{x^2} y^3$

Determine the general solution of the differential equation $\frac{dy}{dx} = \frac{3x^2 + 1}{2y}$

Solve the differential equation $\frac{dy}{dx}=xy$ to find the general solution.

Find the general solution of the differential equation $\frac{dy}{dx} = (x+1)(y-1)$.

Determine the general solution of the differential equation $\frac{dy}{dx} = (x-1)^2(y+3)$

Solve for the general solution of the differential equation $\frac{\text{d}y}{\text{d}x} = \frac{\cos x}{1 + y^2}$

Solve the differential equation $\frac{dy}{dx}=\frac{x^2}{1+y^2}$ giving an implicit general solution.

Find the general solution of the differential equation $\frac{dy}{dx} = y^{1/3} \sin x$

Find the general solution to $\frac{dy}{dx} = \frac{y+2}{x}$.