1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integrate this.

  1. Dec 5, 2006 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant 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))


    3. The attempt at a solution

    I don't know how to integrate u2. Is there a trick involved?
     
  2. jcsd
  3. Dec 5, 2006 #2

    benorin

    User Avatar
    Homework Helper

    www.quickmath.com - powered by webMathematica: this site is very handy and will do algebra (factoring, simplify, partial fraction decomposition, expand), solve equations/inequalities (single or a system), plot equations/inequalities (single or a system), derivatives, definite or indefinite integrals, and do matrix arithmetic/inverses/determinants.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook