Solve Differential Equation y"+3y'+2y=sin(e^x)

[chaose]

Homework Statement

Integrate [e^(-x)*sin(e^x)]dx ?

This is part of the work. I was actually rying to find the general solution to the differential equation y"+3y'+2y=sin(e^x) using the variation of the parameter method.

Homework Equations

Particular solution Y = u1(x)y1(x) + u2(x)y2(x), where u1 and u2 are functions of x, y1 and y2 were determined from the homogeneous version of the equation.

Wronskian = e^(-x)+2e^(-x) = 3e^(-x)

u1 = integral of -(e^x)sin(e^x)/(3e^-x)dx = -1/3 (sin(e^x)-e^xcos(e^x))

The Attempt at a Solution

I don't know how to integrate u2. Is there a trick involved?

 

[benorin]

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