Differential equations

Directions: Solve the following problems. Write your complete solutions on the space provided.

Recall from integral calculus the following properties: SIf (x) + g(x)]dx = S f(x)dx + S g(x)dx S of(x)dx = cf f(x) dx,cER Use these two (2) properties, the definition of Laplace transform, and the formulas derived from the examples in the handout to evaluate the following items: 1. L(5e2x _ x3) 2. L(3 - e-3x + 5 cos 2x) 3. L sin (x + " ) ] Hint: use Sum and Difference of Two Angles Identities (Angles are in radians)