The differential equation of the form

is called separable, if f(x,y) = h(x) g(y); that is,

In order to solve it, perform the following steps:

(1) Solve the equation g(y) = 0, which gives the constant solutions of (S);

(2) Rewrite the equation (S) as

and, then, integrate

to obtain

(3) Write down all the solutions; the constant ones obtained from (1) and the ones given in (2);

(4) If you are given an IVP, use the initial condition to find the particular solution. Note that it may happen that the particular solution is one of the constant solutions given in (1). This is why Step 3 is important.




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