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matematikuvol
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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?