Question

F ''(t) = 2e^t + 5 sint , f(0) = 0, f(π) = 0. Find f(t).?

Answer 1

Step 1:

The function .

Apply integral on each side with respect to .

Apply formula .

Consider .

.

Substitute in .

.

Step 2:

The differential equation is .

Again apply integral on each side with respect to .

.

Apply sum and difference rule in integration .

.

Apply constant rule of integration .

.

Step 3:

.

Substitute in .

.

The equation .

Solution:

The equation .