Solution Of Initial And Boundary Value Function

Problems on Initial and Boundary Value Function:

2. Solve subject to the condition y(0) = y'(0)

Solutions: We have (D² 4D 3)y = e^-x

                  A.E is m² 4m 3 = e^-x

                  (m 1) (m 3) = 0

                   m = -1,-3

Consider the condition y(0) = 1 and y'(0) = 1

Above equations we get;

By solving these equations we get;

     is particular solutions.

3. A particular moves along the x-axis according to the law If the particular is started at x = 0 with an initial velocity of 12 ft/sec, determine x in terms of t.

Solutions: We have (D² 6D 25) = 0 . From the given data. the initial conditions x = 0  when t = 0 and dx/dt = -12 when t = 0.

               A.E is m2 6m 25 = 0

               m = -3± 4i