Question

Solve y’’ – 11y’ + 24y = e^{x} +3x using:

- Reduction of order
- V.C superposition
- Variation of parameters

Answer #1

Solve the differential equation y" + 11y' + 24y = 0

Solve using reduction of order or variation of parameters
4x2y” + 4xy’ + (4x2 – 1)y = F(x)
y1(x) = x -1/2 sin
x and
y2(x) = x -1/2 cos
x
Your answer will come out in terms of integrals involving
F(x).
Find a function F(x) for which you can easily calculate the
necessary integrals in the answer and do the integral

Using variation of parameters, solve: y"-y=e2x

Solve the differential equation by variation of parameters.
5y'' − 10y' + 10y = ex sec(x)
y(x) = ______.

Solve using the method of variation of parameters.
y"+y= sec(x)

Solve the following second order differential equations:
(a) Find the general solution of y'' − 2y' = sin(3x) using the
method of undetermined coefficients.
(b) Find the general solution of y'' − 2y'− 3y = te^−t using the
method of variation of parameters.

Solve the following differential equations by using variation of
parameters.
y''-y'-2y=e3x

solve the linear order y' - 2y = cos(3x). solve for y.

Solve the following systematically using Variation of
Parameters
y''+4y=g(t)

Solve the following systematically using Variation of
Parameters
y''-2y'+y=e^t/(1+t^2)

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