### MAT 394 Self check: ODE

##### First order equations
1. Find general solution $y'=x^2 y$ and solution satisfying Cauchy problem $y(0)=1$.
2. Find general solution $y'+\tan (x)y=\cos(x)$ and solution satisfying Cauchy problem $y(0)=0$.

##### Higher order equations
3. Find general solution to $y''=y^2$ and solution satisfying Cauchy problem $y(0)=0$, $y'(0)=1$.

##### Linear equations of order $\ge 2$
1. Find general solutions of equations \begin{align} &y''-4y=0,\label{eq-1}\\ &y''-4y'+4y=0,\label{eq-2}\\ &y''+4y=0,\label{eq-3}\\ &y''-5y'+6y=0,\label{eq-4}\\ &y''-4y'+5y=0,\label{eq-5}\\ &y^{(4)}-16 y=0.\label{eq-6} \end{align}
2. Solve equations (\ref{eq-1})-(\ref{eq-5}) with the right-hand expressions $e^x$, $e^{2x}$, $\sin (x)$, $\sin (2x)$.
3. Solve (\ref{eq-3}) with the right-hand expression $\tan(2x)$. ##### Systems

Solve this problem

There are resources from Fall 2012 and Spring 2013 classes to study and to check you knowledge of ODE. .