i cant seem to figure this out

It is easy to check that for any value of c, the function y=ce^-2+e^-x

is solution of equation y'+2y=e^-x

Find the value of c for which the solution satisfies the initial condition y(-4)=10

c=?

thanks for any help

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- Apr 8th 2008, 10:23 AMwaite3im having trouble with this one.
i cant seem to figure this out

It is easy to check that for any value of c, the function y=ce^-2+e^-x

is solution of equation y'+2y=e^-x

Find the value of c for which the solution satisfies the initial condition y(-4)=10

c=?

thanks for any help - Apr 8th 2008, 11:01 AMMoo
Hello,

y=ce^-2+e^-x

I guess it's -2x

So $\displaystyle y(x)=c*e^{-2x}+e^{-x}$

$\displaystyle y(-4)=10 \leftarrow 10=c*e^8+e^4$

$\displaystyle c*e^8=10-e^4$

$\displaystyle c=\frac{10-e^4}{e^8}$

This is really awful ! - Apr 8th 2008, 11:06 AMwaite3
that worked your on fire! thanks a lot.