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Math Help - Euler's equation

  1. #1
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    Euler's equation

    the differential equation I have is X^2y'' - 3xy' + 4y = x^2

    Ive used Euler's equation to reduce it to y'' - 4y' + 4y = x^2

    To solve this I know i need yc + yp and I have worked out Yc to equal (A + bx)e^2x

    But its the yp im more worried about... with the x^2 do i have to let x = e^z?

    if i do then I should get e^2x? then the guess i would make for yp would be Ae^2x? but so i need to do this? when i changed it to e^2x it cancelled out...so i tried Axe^2x and it cancelled out again -.-"" what do i do now??
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  2. #2
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    Quote Originally Posted by CookieC View Post
    the differential equation I have is X^2y'' - 3xy' + 4y = x^2

    Ive used Euler's equation to reduce it to y'' - 4y' + 4y = x^2

    To solve this I know i need yc + yp and I have worked out Yc to equal (A + bx)e^2x

    But its the yp im more worried about... with the x^2 do i have to let x = e^z?

    if i do then I should get e^2x? then the guess i would make for yp would be Ae^2x? but so i need to do this? when i changed it to e^2x it cancelled out...so i tried Axe^2x and it cancelled out again -.-"" what do i do now??
    To find the particular solution, use the method of undetermined coefficients: yp = ax^2 + bx + c and your job is to get the values of a, b and c.
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  3. #3
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    So i don't have to tranform the x^2 to e^2z even though i used Euler equation? and i can just solve it as f(x) = x^2 and find the coefficients of A B and C?
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