Homework $5$: First Order Linear Differential Equations

Find the solution the following differential equations and initial value problems, give a valid interval of definition, and identify all transient terms.

$y^{\text{'}}=e^{2x}-y$

$x^2{y}^{\text{'}}+xy=8$

$y^{\text{'}}=2y+x^2+9$

$x{y}^{\text{'}}-y=x^{2}sinx,y()=0$

$x{y}^{\text{'}}+2y=x^3-x,y(1)=2$

$y^{\text{'}}-\frac{2}{x}y=x^2$