IB Mathematics Applications & Interpretation Question Type 3: Solving a Separable Differential Equation to Obtain the General Solution Exercises

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

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 $$\frac{dy}{dx}=\frac{y+2}{x}$$.