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Solve the differential equation or initial value problem using the method for undetermined constants and variation of parameters.

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Solve the differential equation using the method of variation of parameters.
Solve the differential equation or initial-value problem using the method for undetermined constants.
y''-4y=e^x cosx y(0)=1, y'(0)=2

y''+y'- 2y=x - sin 2x y(0)=1, y'(0)=0

y'' + y = cot x 0<x<pi/2
See attached file for full problem description.

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ODEs and IVPs are solved. The solution is detailed and well presented.

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Solve the differential equation or initial-value problem using the method for undetermined constants
8.
(1) First the solution to the homogeneous differential equation
.
Its characteristic equation has 2 real roots, which are . So the solution is

(2) the particular equation to the differential equation
Assume it has the particular solution has the form of
Plug into the ...

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