Y\" - 2y\' + 2y = e -t sin 2t + 2t + te -1 sin t Determine the complementary sol

Question

Y" - 2y' + 2y = e -t sin 2t + 2t + te -1 sin t Determine the complementary solution. List the form of particular solution prescribed by the method of undertermined co-efficients; you need not evaluate the constants in the assumed form. [Hint: In Exercises 20 and 22, rewrite the hyperbolic functions in terms of exponential functions In Exercise 21, use trigonometric identities.]

Explanation / Answer

1.for complementary solution D^2-2D+2=0 =>D= 1+i or 1-i y=e^t*( A cost+ B sint) or it can also be written as : y= C1*e^[(1+i)t]+C2*e^[(1-i)t] 2. The particular solution can be obtained by solving= R.H.S./ (D^2-2d+2)

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