d2ydx2 y e2XSolutiony1e2x The characteristic equation is k

d^2y/dx^2 - y = e^2X

y\'\'-1=e^2x

The characteristic equation is

k² -1=0 with roots 1 and -1.

So the C.F is

A e^x +B e^-x

Trying C e^2x for a particular integral , we get

4C e^2x -e^2x =e^2x , so C =1/3

Hence the general solution of the equation is

y(x) = A e^x +B e^-x +1/3 e²^x

$d^2y/dx^2 - y = e^2XSolutiony\'\'-1=e2x The characteristic equation is k2 -1=0 with roots 1 and -1. So the C.F is A ex +B e-x Trying C e2x for a particular int$

d2ydx2 y e2XSolutiony1e2x The characteristic equation is k

Solution

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