Final answer:
A separable differential equation can be written in the form dy/dx = g(x) f(y) and can be solved using the method of separation of variables.
Step-by-step explanation:
A separable differential equation is a type of differential equation that can be written in the form dy/dx = g(x) f(y). It can be solved by using the method of separation of variables, which involves isolating the variables on each side of the equation and integrating. Let's say we have the equation dy/dx = x^2 y. To solve this equation, we can separate the variables by writing it as dy/y = x^2 dx. By integrating both sides, we get ln|y| = (1/3)x^3 + C, where C is the constant of integration. Finally, we can solve for y by taking the exponential of both sides: y = e^((1/3)x^3 + C).