Calculus AB

Solve the differential equation:

dy/dx= (x^2+y^2)/(2xy)

I know how to solve this type of problem, but I am struggling getting all of the x's and y's on different sides of the equation. Thank you for your help.

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asked by Jake
  1. Note that the right-hand side is homogeneous (i.e. the total of exponents of x and y equals 2 for all terms), so a substitution of u=y/x will render the equation separable.

    u=y/x
    udx+xdu=dy
    dy/dx = u+x*du/dx
    ...

    Post if you have difficulties.

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