Differential Equations Answers

Use the Laplace transform to solve the given initial value problem.

y^(4)−256y=0; y(0)=43, y′(0)=104, y′′(0)=432, y′′′ (0)=1,024


Enclose arguments of functions in parentheses. For example, sin(2x).

y(t)= _______________

Find the inverse Laplace transform L−1{F(s)} of the given function.

F(s) = 8s^2 − 12s + 144 / s(s^2+36)


Your answer should be a function of t. Enclose arguments of functions in parentheses. For example, sin(2x).

L−1{F(s)}= ___________-

Find the Laplace transform of the piecewise continuous function
f(x) = {1, 0 ≤ t < 1}
{-3e^-t, t ≥ 1}

Find the general solution of
y" + 3y' + 2y = 1/(1+e^x)

(x+2y-1)dx - (x+2y+1) dy =0

(2t×siny+e to the power t×y to the power 3)dt+(t to the power 2×cosy+3×y to the power 2×e to the power t)dy=0

1. Find the inverse Laplace transform ℒ-^1 { e^-5s / s^2 - 25 }

2.Find the Laplace transform of the given function.

f(t) = {1, 0 ≤ t < 6
{ 0, t ≥ 6

Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).


L {f(t)} = __________ , s>0.

1. Use the Laplace transform to solve the given initial value problem.

y^4) − 81y = 0; y(0) = 20, y′(0) = 39, y′′(0) = 108, y′′′ (0) =1 89


Enclose arguments of functions in parentheses. For example, sin(2x).

y(t) = ___________


2. Find the Laplace transform of the function:

f(t) = { 0, t < 4
{ t^2 - 8t + 9, t is greater than or equal 4

Find the Laplace transform Y(s)=L{y} of the solution of the given initial value problem.

y′′ + 4y = { t, 0 ≤ t < 1
{ 1, 1 ≤ t < ∞, y(0) = 3, y′(0) = 3


Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).

Y(s)= _______________