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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.

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  • $\begingroup$ Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$. $\endgroup$ – John Wayland Bales Mar 13 at 16:47
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Start with taking the derivative of your general solution and then plug in the respective initial values.

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  • $\begingroup$ Was that helpful? $\endgroup$ – Maths2020 Mar 13 at 16:57

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