Question
Asked Jul 1, 2019
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Using the method of undetermined coefficients, find the general solution to the differential equation:

y'''-3y"+3y'-y=4et

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Expert Answer

Step 1

The given differential equation is y′″ - 3y″ - y = 4e                                   ...... (1)

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The auxiliary equation is m2-3m2 3m-1=0 (т-1) -0 (т-1)(т-1)(т-1)-0 m 11,1 Therefore, the complimentary solution is y =Ge +C,te +Ctfe Obtain the particular solution of e' as follows. 1 4e D3-3D23D-1 1 -4e (1)-3(1)+3(1) ( D-1) 1 .4e 1-3+3-1 4e 0

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Step 2

Now multiply the numerator with t and differentiate the denominator.

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4te 3D2-6D+3 4te 3(1)6(1)+3 (D 1 4te 3-6+3 4te 0

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Step 3

Again multiply the numerator with t and d...

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4t e yp6D-6 41e 6(1)-6 4r e ( D 1) 0

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