# RS Aggarwal Class 12 Differential equations with variable separable PDF

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### What are Differential equations with variable separable?

A differential equation is said to be variable separable if it can be written in the form:

dy/dx = f(x)g(y)

where f(x) and g(y) are functions of x and y respectively.

Solving a variable separable differential equation involves separating the variables x and y, by dividing both sides of the equation by g(y) and then multiplying both sides by dx to get:

dx/f(x) = dy/g(y)

This equation can then be integrated on both sides to find the general solution of the differential equation.

An example of a variable separable differential equation is: dy/dx = x*y^2

This can be solved by dividing both sides by y^2 and then multiplying both sides by dx to get:

dx/x = dy/(y^2)

Integrating both sides we get:

∫dx/x = ∫dy/(y^2) + c

Where c is the constant of integration.

This method of solving variable separable differential equations is particularly useful when the functions f(x) and g(y) can be easily integrated, or when a general solution is needed rather than a specific solution.

CH-19-Differential-equations-with-variable-separable

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