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Math Help - differentiable equation problem!

  1. #1
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    differentiable equation problem!

    Solve the differential equation below by making the change of variable u = y/x. (Use K to represent any constant and place "+" before it.)

    so when you replaced with u, you get dy/dx = u + e^(5u)

    how do you solve that since you still have dy/dx and not a du..?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by khood View Post
    Solve the differential equation below by making the change of variable u = y/x. (Use K to represent any constant and place "+" before it.)

    so when you replaced with u, you get dy/dx = u + e^(5u)

    how do you solve that since you still have dy/dx and not a du..?
    Since u=\frac{y}{x}\implies y=ux, we see that \frac{\,dy}{\,dx}=u+x\frac{\,du}{\,dx} (by product rule)

    Thus, the DE becomes x\frac{\,du}{\,dx}+u=u+e^{5u}\implies x\frac{\,du}{\,dx}=e^{5u}. Now apply the technique of separation of variables.

    Can you take it from here?
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