Calculus AB
posted by Jake on .
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.

Note that the righthand 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.