1.

3. Solve the IVP using the Laplace transform y' - 2y =4, given that y(0) = 1 *​

Answer»

Given: y' - 2y = 4,

           y(0) = 1 (this is initial value)

To find: y(t)

solution:

IVP means initial value Problem

step 1: take Laplace transform for given EQUATION:

           (sY(s) - y(0)) -2Y(s) = 4................................equation -1

     as,  y(0) = 1 (given)

so, put y(0) = 1 in equation -1, we GET

           (sY(s) - 1) -2Y(s) = 4

           sY(s) -1- 2Y(s) = 4

            Y(s) (s - 2) - 1 = 4

            Y(s) (s - 2) = 4+1

            Y(s) (s - 2) = 5

            Y(s) = \frac{5}{(s-2)}....................................................................equation -2

step 2: take Laplace inverse of equation -2, we get;

             y(t) = 5 e^{2t}

so the final ANSWER is y(t) = 5 e^{2t}


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