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

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

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

Find the general solution of $\frac{dy}{dx}=\frac{x+1}{y-1}\,.$

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

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

Solve for the general solution of $\frac{dy}{dx}=\frac{\cos x}{1+y^2}\,.$

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

Solve for $y$ in the general solution of $\frac{dy}{dx}=e^x y^2\,.$

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

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

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

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