IB Mathematics Analysis and Approaches Question Type 4: Solving with the Integrating Factor Exercises

Solve the linear ODE $y^{\prime }+(\tan x)y=\sin x$ for the general solution $y(x)$.

Solve $y^{\prime }+(\tan x)y=\sec x\tan x$ given $y(0)=0$.

Solve the differential equation $y^{\prime }+\frac{1}{x}y=\frac{\sin x}{x}$ for $x>0$, given that $y(\pi )=0$.

Solve the differential equation $y^{\prime }=\frac{dy}{dx}=\cos x+y\tan x$ for $y(x)$.

Solve $y' + \dfrac{3}{x} y = 4x^2$ for the general solution $y(x)$ (assume $x>0$).

Solve the ODE $y^{\prime }+(1-\tan x)y=\sec x$ for the general solution $y(x)$.

Solve $x{y}^{\prime }+y=x^2$ with $y(1)=1$. [6 marks]

Solve $y^{\prime }+2y=e^{-x}$ with the initial condition $y(0)=0$.

Solve $y^{\prime }-y=e^{2x}$ with $y(0)=0$.

Solve $y^{\prime }+\frac{2}{x}y=3x$ with $y(1)=2$.

Solve $y^{\prime }+2xy=x$ for the general solution $y(x)$.

Solve $y^{\prime }+\frac{1}{1+x}y=\frac{2}{1+x}$ subject to $y(0)=0$.

Solve the differential equation $y' = \cos(x) + y\tan(x),$ given the boundary condition $y(0)=1$.

Solve $y^{\prime }-\frac{2}{x}y=x^2$ subject to $y(1)=0$.