Give the general solution to the following differential equation and use the general solution to solve this initial value problem:
$$y''-y=0,\quad
y(1)=1+e,\quad y'
(1)=-1+e,
\quad y=e^{rt}$$
I found that the general solution is equal to
$$y(t)=C_1e^{-t} + C_2e^{t}$$
However I'm not sure how to find the solution to the initial value problem. I thought that $C_1=1$ and $C_2=-1$ might be the solution.
Thanks in advance for any help.
Best Answer
Start with taking the derivative of your general solution and then plug in the respective initial values.