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Math Help - First order DE problem

  1. #1
    DCU
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    First order DE problem

    For any of the constant value k, the function y is a solution of the last equation.

    Find p and q.

    I've tried subbing in y and y' but I need P and Q explicitly. Don't know what to do.
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  2. #2
    DCU
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by DCU View Post
    For any of the constant value k, the function y is a solution of the last equation.

    Find p and q.

    I've tried subbing in y and y' but I need P and Q explicitly. Don't know what to do.

    The key is the hint they gave you. It is true for every value of k

    So you get
    \cos(x)-\frac{k}{x^2}+P(x)\left(\sin(x)+\frac{k}{x} \right)=Q(x)

    This is true for every value of k so pick some easy ones like
    k=0,k=1 and solve for P and Q.
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