Question

I would appreciate an explanation

Lecture 12 The method of undetermined coefficients works for which of these DE? A. y + y = tan(t) B. 2y" +) y = rith C. y" +ty' + y = 1 D. Y" - 5y' = 2 E. y' = t In(t) F. None of the above If y = Ae3t+ Besolves y" + ay'+by = 0. What is the general form for a particular solution, with minimum constants for y" + ay' + by = 5te3t? Yp = Ctet B. Yp = Ctet C. Yp = (Ct + D)e 36 D. Yp = (Ct + D)Etest E. Yp - (Ct + D)test F. None of the above.

Answer 1

A) since we cannot guess yolt) for tant. B) we can't guess "pet) for the ( Here 4 is unknown variable. Tips so we can not that homogenous system y+ty4 y = D. 80 . We can not apply undetermined coefficient methay, d) we can't guess & Solt) for t dn(t) so we can't apply undetermine coofficient metta. F) None of the above (F) right answer. .: Ya A et ts et usest, et sis linearly independent 1 8 olution of homogenuory system of problem. again given yıtay't by = 5tetit 8o initial guess yolt) is (At+B) et 37 1. Which is linearly independent of {et, et Hence Y(t) = o(etto) est is right and we CScanned with CamScanner