Use Laplace transform method to solve the following initial
value problems
(a) d2y/dt2 + y = e^ −t ; y(0) = 0, y′ (0) = 0.
(b) d2y/dt2+ y = t subject to the initial
conditions y(0) = 0, y′ (0) = 2
(c) dy/dt + 2y = 4e 3t subject to the initial
condition y(0) = 1.
Use the Laplace transform to solve the following initial value
problem,
y′′ − y′ − 30y = δ(t − 7),y(0) = 0, y′(0) = 0.
The solution is of the form ?[g(t)] h(t).
(a) Enter the function g(t) into the answer box below.
(b) Enter the function h(t) into the answer box below.
1. Use a Laplace transform to solve the initial value problem:
9y" + y = f(t), y(0) = 1, y'(0) = 2
2. Use a Laplace transform to solve the initial value problem:
y" + 4y = sin 4t, y(0) = 1, y'(0) = 2