Calculus
Separation of variables
Get all the y's on one side, all the x's on the other, then integrate both.
For a separable DE dy/dx = f(x)g(y): get all y's on one side, all x's on the other, and integrate.
Try it
dy/dx = xy
dy/y = x dx. ln|y| = x²/2 + C. y = A·e^(x²/2).