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## Homework Statement

solve the initial value problem:

y

^{''}+8.4y

^{'}+17.64y=e

^{-4.2x}

y(0)=1, y

^{'}(0)=1

y(x)=?

## Homework Equations

y=y

_{c}+y

_{p}

## The Attempt at a Solution

The way I tried to achieve is to solve the corresponding homo equation first:

y

^{''}+8.4y

^{'}+17.64y=0, which gives y

_{c};

y

_{c}=c

_{1}e

^{-4.2x}+c

_{2}e

^{-4.2x}x

Then try to find y

_{p}, generally I would assume a y

_{p}=Ae

^{-4.2x}, but from the y

_{c}got above, clearly y

_{p}=Ae

^{-4.2x}or y

_{p}=Ae

^{-4.2x}x is not good. If I add one more 'x' in y

_{p}assumption,in which it seems A has to be 0, which is not right either...

Any idea? Or I made some mistake?

Meric.