Separable differential equations Find the general solution of the following equations.

, where y > 0

Problem 24E

Separable differential equations Find the general solution of the following equations.

, where y > 0

Answer;

Step 1;

DEFINITION : A differential equation is said to be of type “variable separable” if it can be expressed in such a way , so that the coefficient of dx is a function of of x alone and the coefficient of dy is a function of y alone.

The general form of such differential equation can be written as

f(x) dx = g(y)dy ……………….(1)

Integrating both sides and adding an arbitrary constant C , we get the general solution as

f(x)dx = +C

Working rule of solving by the method of separation of variables;

- Write the given differential equation in the form

f(x) dx = g(y)dy

That is make the coefficient of dx as an expression of x alone and that of dy as an expression of y alone

2. Integrate both sides and add an arbitrary constant to any one side and get the general solution.