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Math Help - Solving a first order DE

  1. #1
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    Solving a first order DE

    Hello,

    I am trying to solve this problem:
    x(dy/dx)-2y=x^15
    By bringing this to the standard form I get:
    (dy/dx)-(2/x)y=x^14
    Now I multiply the equation by (1/x^2)
    I get the form d/dx(y/x^2)=(x^12)
    Integrating both sides I get: (y/x^2)=((x^13)/13)+C(x^2)

    Now I tried using the condition y(1)=-2 to get the value of C. However, every time I get the value of C to be 1, unfortunately this is not the right answer.

    Where am I going wrong, any help would be highly appreciated.

    Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sgupta View Post
    Hello,

    I am trying to solve this problem:
    x(dy/dx)-2y=x^15
    By bringing this to the standard form I get:
    (dy/dx)-(2/x)y=x^14
    Now I multiply the equation by (1/x^2)
    I get the form d/dx(y/x^2)=(x^12)
    Integrating both sides I get: (y/x^2)=((x^13)/13)+C(x^2)

    Now I tried using the condition y(1)=-2 to get the value of C. However, every time I get the value of C to be 1, unfortunately this is not the right answer.

    Where am I going wrong, any help would be highly appreciated.

    Thanks!
    Assuming what you have for the general solution is correct:

    \frac{y}{x^2}=\frac{x^{13}}{13}+Cx^2

    Put x=1:

    y(1)=-2=\frac{1}{13}+C

    CB
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