13: Intro to Differential Equations

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.

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

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

$\left(y^{\prime\prime}\right)^2+6e^{t}y^{\prime}=4t$

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 $\frac{dy}{dx}=-2x+5x^2$.