Question

Slove the first - order differential equation by any appropriate method.

Answer 1

Step 1:

The differential equation is .

Use linear method of differential equation :

is the standard form of first - order linear differential equation.

Where P  and Q  are continuous functions of x.

To solve the linear differential equation.

(1) is the integration factor.

(2) is the general solution of the differential equation.

Step 2:

The differential equation is .

Convert this equation into standard form of first - order linear differential equation.

From above, .

Solve the linear differential equation .

(1)

Find the integration factor.

Step 3:

(2)

Find the general solution.

Now solve for .

Consider .

Substitute and in above integration.

Substitute in the above expression.

Substitute the values in the general solution.

Solution :

The general solution of the differential equation is .