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## Homework Statement

Solve ODE

[tex]y''-y=e^{-t}[/tex]

[tex]y(0)=1, y'(0)=0[/tex]

## Homework Equations

## The Attempt at a Solution

Homogenuous solution

[tex]t^2-1=0[/tex]

[tex]y=C_1e^t+C_2e^{-t}[/tex]

From

[tex]y(0)=1, y'(0)=0[/tex]

[tex]y=\frac{1}{2}e^t+\frac{1}{2}e^{-t}[/tex]

How from that get complete solution?