Question

Find the particular solution of the differential equation that satisfies the boundary condition.

Differential Equation                                         Boundary condition

y' + y tan x = sec x + cos x                                   y (0) = 1

Answer 1

Step 1:

The differential equation is and Boundary condition is .

The differential equation is a first order linear differential equation.

Solution of first order linear differential equation is

.

Compare with standard form of differential equation.

and .

Step 2:

First find .

Step 3:

The solution of differential equation is .

Substitute and in above equation.

Step 4:

The solution of the differential equation is .

Boundary condition is .

Substitute and in the solution of the differential equation.

Substitute in the solution of the differential equation.

Solution:

The solution of the differential equation is .