APM346 Self check: ODE
This is not a home assignment!
First order equations
- Find general solution $y'=x^2 y$ and solution satisfying Cauchy problem $y(0)=1$.
Find general solution $y'+\tan (x)y=\cos(x)$ and solution satisfying Cauchy problem $y(0)=0$.
Higher order equations
Find general solution to $y''=y^2$ and solution satisfying Cauchy problem $y(0)=0$, $y'(0)=1$.
Linear equations of order $\ge 2$
- 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}
- Solve equations (\ref{eq-1})-(\ref{eq-5}) with the right-hand expressions $e^x$, $e^{2x}$, $\sin (x)$, $\sin (2x)$.
- Solve (\ref{eq-3}) with the right-hand expression $\tan(2x)$.
Systems
There are resources from Fall 2012 and Spring 2013 classes to study and to check you knowledge of ODE. .