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Math Help - Method of Undetermined Coefficients

  1. #1
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    Method of Undetermined Coefficients

    Use the method of undetermined coefficients to solve the following differential equation: y''+y'=4x

    y(x)=______ +C1+______ C2_____
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  2. #2
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    Quote Originally Posted by killasnake View Post
    Use the method of undetermined coefficients to solve the following differential equation: y''+y'=4x

    y(x)=______ +C1+______ C2_____
    I'm a little rusty on Undetermined Coefficients, but you want to start by arbitrarily choosing a function in the same form as the inhomogeneous one you're giving.

    For example, y_{p}=ax+b should work for this situation.
    Find the derivative, and second derivative so that
    y_{p}'=a
    and y_{p}''=0

    Now that you have that, you can plug in these functions where they are needed in the original. So, you should get

    a+0=4x

    I'm sort of confused, and maybe you left out a y factor, but if this is right, then you get 0 for both coefficients.

    So, assuming that you did write the original equation correctly, then the solution to the inhomogeneous part is as follows: y_{p}(x)=0

    You can solve for y_{h}(x) using your typical method of solving for \lambda_{1} and \lambda_{2}

    If you need help with the homogeneous solution, just post, and I will help you out.
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