Question

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

y′′−2y′−143y=0; y(0)=8, y′(0)= 32

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

Answer #1

Use the Laplace transform to solve the given initial value
problem.
y′′−8y′−105y=0; y(0)=8, y′(0)= 76
Enclose arguments of functions in parentheses. For example,
sin(2x).

Differential Equations: Use the Laplace transform to solve the
given initial value problem:
y′′ −2y′ +2y=cost;
y(0)=1,
y′(0)=0

Solve the initial value problem y′=[10cos(10x)]/[3+2y], y(0)=−1
and determine where the solution attains its maximum value (for
0≤x≤0.339). Enclose arguments of functions in parentheses. For
example, sin(2x).
y(x)=
The solution attains a maximum at the following value of x.
Enter the exact answer.
x=

Use Laplace transform to solve the following initial value
problem: y '' − 2y '+ 2y = e −t , y(0) = 0 and y ' (0) =
1
differential eq

Find the solution of the initial value problem
y′′+4y=t2+7et y(0)=0, y′(0)=2.
Enter an exact answer.
Enclose arguments of functions in parentheses. For example,
sin(2x).

Solve the initial value problem using
Laplace transform theory.
y”-2y’+10y=24t,
y(0)=0,
y'(0)= -1

Use the Laplace transform to solve the given initial-value
problem. y'' + y = δ(t − 8π), y(0) = 0, y'(0) = 1

Use the Laplace transform to solve the given initial-value
problem. y'' − 7y' + 12y = (t − 1), y(0) = 0, y'(0) = 1

Use the Laplace transform to solve the given initial-value
problem. Use the table of Laplace transforms in Appendix III as
needed.
y'' + 25y = cos 5t, y(0) =
3, y'(0) = 4

Find the Laplace transform Y(s)=L{y} of the solution of the
given initial value problem.
y′′+9y={t, 0≤t<1 1, 1≤t<∞, y(0)=3, y′(0)=4
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
Y(s)=

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