Question

Solve the initial-value problem for linear differential equation

y^{''} + 4y^{'} + 8y = sinx; y(0) = 1,
y^{'}(0) = 0

Answer #1

solve the initial value problem
y''+8y=cos(3t), y(0)=1, y'(0)=-1

Solve the following differential equations
y''-4y'+4y=(x+1)e2x (Use Wronskian)
y''+(y')2+1=0 (non linear second order equation)

Solve the given initial-value problem.
y'' + 7y' −
8y =
16e2x, y(0)
= 1, y'(0) = 1

Solve the initial value problem y''+4y'+4y=0, y(-1)=5,
y'(-1)=5

Solve the 1st-order linear differential equation using an
integrating fac-
tor. For problem solve the initial value problem. For each
problem, specify the solution
interval.
dy/dx−2xy=x, y(0) = 1

Solve the initial value problem. Explain and show all steps.
y'' - 4y' +4y = 0
where y(0) = 1 and y'(0) = 2

2. Solve the initial-value problem: y′′′ + 4y′ = t, y(0) = y′(0)
= 0, y′′(0) = 1.

Solve the initial value problem
y"+2y'-8y=14e^(3t)
y(0)=8, y'(0)=6

Use the Laplace transform to solve the following initial value
problem:
y′′ + 8y ′+ 16y = 0
y(0) = −3 , y′(0) = −3
First, using Y for the Laplace transform of y(t)y, i.e., Y=L{y(t)},
find the equation you get by taking the Laplace transform of the
differential equation
__________________________ = 0
Now solve for Y(s) = ______________________________ and write the
above answer in its partial fraction decomposition, Y(s) = A /
(s+a) + B / ((s+a)^2)
Y(s) =...

Use the Laplace transform to solve the following initial value
problem
y”+4y=cos(8t)
y(0)=0, y’(0)=0
First, use Y for the Laplace transform of y(t) find the
equation you get by taking the Laplace transform of the
differential equation and solving for Y:
Y(s)=?
Find the partial fraction decomposition of Y(t) and its
inverse Laplace transform to find the solution of the IVP:
y(t)=?

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