Question

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

Differential Equation                                        Boundary condition

Answer 1

Step 1 :

An integrating factor for the first-order linear differential equation

is

The solution of the differential equation is

Step 2 :

The equation is and the boundary condition is .

Compare the equation with .

and .

Find the integrating factor :

Step 3 :

Find the solution of the differential equation :

Substitute the boundary condition in above equation.

Substitute  in equation (1).

The solution of the differential equation is

Solution :

The solution of the differential equation is