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
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Please see the attached file for the complete solution.
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Solve the differential equation or initial-value problem using the method for undetermined constants
(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 ...
ODEs and IVPs are solved. The solution is detailed and well presented.