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Math Help - Solving differential equations with conditions

  1. #1
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    Solving differential equations with conditions

    Hello, I have a question xy’ = y ; y = cx; y=pi when x = 2. I have to verify that the given function is a solution to the DE. Also find the c that satisfies the condition.

    So here I put y = pi and x =2 for the xy' = y.

    So i got 2y'= pi which equals to y'= pi/2.

    And I found out that y= (pi/2)x + C. So since I am trying to find C in y=Cx, Is the answer (pi/2)??

    Thank you.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solving differential equations with conditions

    To verify the given solution y=cx satisfies the given ODE, compute y'=c and now substitute for both into the ODE:

    x\cdot c=cx

    This is true, so the solution is valid.

    To find the c that satisfies the given initial condition, simply write:

    y(2)=c\cdot2=\pi\,\therefore\,c=\frac{\pi}{2}
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