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$

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

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

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}$