Question

Find the particular solution that satisfies the initial condition.

Differential equation                                      Initial condition

Answer 1

Step 1:

The differential equation is and the initial condition is .

Homogenous differential equation:

If is a homogenous differential equation, then to find the solution of the differential equation, we substitute , where is differentiable function of .

Consider .

The degree of and is 1.

The differential equation is homogenous differential equation of degree 1.

Substitute and in the differential equation.

Step 2:

Integrate on each side.

If then .

Substitute in the solution of the differential equation.

Solution of the differential equation is .

The initial condition is .

Substitute and in .

Substitute in the solution.

Solution of the differential equation is .

Solution:

Solution of the differential equation is .