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 = (1+y^2)/(1+x^2) separates to dy/(1+y^2) = 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.