The simplest type of ODE to solve. If dy/dx = f(x)*g(y), then dy/g(y) = f(x)*dx. Integrate both sides: integral of dy/g(y) = integral of f(x) dx + C. Key examples: dy/dx = e^(x+y) = $e^x$ * $e^y$, so e^(-y) dy = $e^x$ dx, giving -e^(-y) = $e^x$ + C. Also dy/dx = $\frac{1+y^2}{(1+x^2)}$ separates to $\frac{dy}{1+y^2}$ = $\frac{dx}{1+x^2}$, giving arctan(y) = arctan(x) + C. Watch for division by zero: if g(y0) = 0, then y = y0 is a singular solution that may be lost during separation. Always check if constant solutions exist.