Question

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

Answer 1

Step 1:

The first order differential equation is .

The standard form of linear differentiation equation is  .

Solve the differential equation by converting into linear differentiation equation.

Divide each side by .

Step 2:

Consider .

Apply derivative on each side with respect to .

Substitute and in .

The above equation is in the form of linear differentiation equation .

Compare with .

Where and .

In linear differentiation, substitute .

.

Comments

Contd...

Step 3:

The solution of linear differentiation equation is .

Substitute and .

Back substitute in .

.

Solution:

The solution is .