# find the value that satisfies intial conditions

• August 18th 2009, 11:31 AM
dat1611
find 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?
• August 18th 2009, 02:34 PM
pickslides
Quote:

Originally Posted by dat1611

y+2y=e^–x

Are you sure you don't mean $y'+2y=e^{–x}$ ?

Quote:

Originally Posted by dat1611

y=ce^–2x+e^–x

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

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

Using $y(-3)=4$

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

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

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

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

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

Therefore

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