State the order of the differential equation and indicate if it is linear or nonlinear. 
${\left(y^{\prime \prime }\right)}^2+6e^t{y}^{\prime }=4t$

Solve the differential equation $e^{x}y\frac{dy}{dx}=e^{-y}+e^{-5x}-y$ by separation of variables.

Solve the differential equation $e^{x}y\frac{dy}{dx}=e^{-y}+e^{-4x}-y$ by separation of variables.

State the order of the differential equation and indicate if it is linear or nonlinear. 

$y^{{}^{\prime \prime \prime }}+3xy=4\sqrt{x}$

State the order of the differential equation and indicate if it is linear or nonlinear. 

$\frac{d^{2}y}{d{x}^2}-\left(\frac{dy}{dx}\right)(1-x)=2$

State the order of the differential equation and indicate if it is linear or nonlinear. 

$y^{\prime }\bullet y=3e^t$

Find the particular solution to the differential equation $y^{\prime }=2e^t+4t$ given the initial condition $y\left(0\right)=1$.

Find the general solution to the differential equation $\frac{dy}{dx}=-2x+5x^2$.

Find the particular solution to the differential equation $y^{\prime }=2\sin x+3\cos x$ given the initial condition $y\left(0\right)=4$.