Phantom L.

asked • 03/19/18

Differential Equation Problem: Undetermined Coefficient

Determine the specific solution of the following initial-value problems. Use the method of undetermined coefficients to find the particular solution.

y'' - 2y' + 2y = x3 - 5, y(0)=6 and y'(0)=0

Note: so the general form is y=ex(C1cos(x) + C2sin(x)) and I assume Yp = Ax3 -B? Is this the right guess? Or does it have to be Yp = Ax3 + Bx2 + Cx -5? and for the initial value, do I have to plug them in to the Yp's?

1 Expert Answer

By:

Bobosharif S. answered • 03/19/18

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Mathematics/Statistics Tutor

Phantom L.

I found that Yp=(1/2)x3 + (3/2)x2 + (3/2)x - 5/2     (A=1/2 B=3/2 C=3/2 and D=-5/2)
 
For the initial value, do I just plug in the 0 for the x's in the Yp? and derive Yp to do the same thing for Y'(0)=0?
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03/19/18

Bobosharif S.

Yp(x) is a particular solution of the inhomogeneous equation and the general solution of the equation is yG(x)=y(x)+yp(x). Initial conditions y(0)=6 and y'(0)=0 are for the general solution yG(x)
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03/19/18

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