It is easy to check that for any value of c, the function

y=ce^–2x+e^–x

is solution of equation

y+2y=e^–x

Find the value of c for which the solution satisfies the initial condition y(–3)=4

can someone solve this one?

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- Aug 18th 2009, 11:31 AMdat1611find the value that satisfies intial conditions
It is easy to check that for any value of c, the function

y=ce^–2x+e^–x

is solution of equation

y+2y=e^–x

Find the value of c for which the solution satisfies the initial condition y(–3)=4

can someone solve this one? - Aug 18th 2009, 02:34 PMpickslides
Are you sure you don't mean $\displaystyle y'+2y=e^{–x}$ ?

$\displaystyle y=ce^{-2x}+e^{-x}$

Using $\displaystyle y(-3)=4$

$\displaystyle 4=ce^{-2\times -3}+e^{-(-3)}$

$\displaystyle 4=ce^{6}+e^{3}$

$\displaystyle 4-e^{3}=ce^{6}$

$\displaystyle \frac{4-e^{3}}{e^{6}}=c$

$\displaystyle c=\frac{4-e^{3}}{e^{6}}$

Therefore

$\displaystyle y=\left(\frac{4-e^{3}}{e^{6}}\right)e^{–2x}+e^{–x}$