Given that a differential equation

y'' + p(x)y' + q(x)y = r(x) has three solutions sin x, cos x, and sin 2x. Find yh. (yh is the corresponding homogeneous solution)

Find the form for a particular solution (y sub p) to the following differential equation.

y'' + 2y' - 3y = e^(-3x) + x^2 * e^x

Decide whether the method of undertermined coefficients can be applied to find a particular solutions of the given equations. (Explain)

a) y'' + 3y' - y = tan x b) y'' + xy' + y = sin x

Use the method of undetermined coefficients to solve the following differential equation.

y'' + 2y' - 3y = 9x - 10 sin x y(0)=0 y'(0)=4

Find a general solution on (-pi/2,pi/2) to y''+y=tan x

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Solve Using Derivatives

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inverse laplace tranform

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Determine the Laplace transform of the function.

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Exponential Order

Show that a) ___* is not of exponential order, and b) ___* is of exponential order *Please see attachment to fill in blanks

Find Laplace Transform of sin(t)/t

Find Laplace Transform of sin(t)/t. See attached file for full problem description.