Question

 Solve the boundary-value problem, if possible.

Answer 1

Step 1 :  

The differential equation is and the boundary conditions are

.

The auxiliary equation is .

Find roots of the auxiliary equation.

The roots of the auxiliary equation are .

The general solution is .

Step 2 : 

Substitute the boundary condition in equation (1)

Substitute the boundary condition in equation (1)

Since is can not be determined, the differential equation has no solution.

Solution :

The differential equation has no solution.