y^(4) - 5y''+ 4y=e^x-xe^2x

Find the general solutionypof the given equation

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- April 19th 2009, 04:28 PMbearej50Nonhomogeneous Equations and Undetermined Coefficients
*y*^(4) - 5*y''*+ 4*y*=*e*^*x*-*x**e*^2*x*

Find the general solution*yp*of the given equation - April 19th 2009, 06:26 PMCalculus26
Solve the homogeneous equation

your soln's are e^2x, e^(-2x) , e^x and e^(-x )

for yp for the e^x term you'd normally have an Ae^x term but it is a homog solution so use Ax*e^x

For x^e(2x) normally you would have a Bxe^(2x) and a Ce^(2x)

but since e^(2x) is a solution to the homogeneous eqn

multiply each by x so you'll have Bx^2e^(2x) and Cxe^(2x)

yp = Axe^x + Bx^2*e^(2x) + Cx*e^(2x)

Now you're ready to go to work