Solve d2y/dx2-2dy/dx+y=xexsinx

Variation of Parameters. The Wronskian method. Do you like this method?
How to solve a non-homogenous second order linear differential equation?
A method to skip "Let y=e^(mx)" for complementary function but it is fast and accurate.
Solve d2y/dx2-2dy/dx+y=0 by inserting the dummy "m", fast and accurate. The complementary function for the associated homogenous equation, a faster way.
This method is applicable for all homogenous second order linear differential equations.

Have no ideas on what is the general function to be used for the particular integral? The Wronskian determinant could help!
General form of yp=A(x)u1(x) + B(x)u2(x) where A(x) = integral of 1/W u2(x) f(x) dx while B(x) = integral of 1/W u1(x) f(x) dx and W=determinant of [{u1(x), u2(x)}, {u'1(x), u'2(x)}].
Note that, u(x) are the functions obtained from the derived complementary function.

Apply DI method in integration. A shortcut for integration by parts!

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#Differential #Equation