If a differential equation is separable, then it is possible to solve the equation using the method of separation of variables. Check for any values of y that make g(y)=0. ... Rewrite the differential equation in the form dyg(y)=f(x)dx.

Can you solve non separable differential equations?

In mathematics, an inseparable differential equation is an ordinary differential equation that cannot be solved by using separation of variables. To solve an inseparable differential equation one can employ a number of other methods, like the Laplace transform, substitution, etc.

Can any differential equation be solved?

Not all differential equations will have solutions so it's useful to know ahead of time if there is a solution or not. If there isn't a solution why waste our time trying to find something that doesn't exist? This question is usually called the existence question in a differential equations course.