Expert answers to "Use the method of undetermined coefficients to find..." - Plainmath

Vikolers6

Answered question

2021-12-20

Use the method of undetermined coefficients to find one solution of

y^{″} - 10 y^{'} + 17 y = 8 e^{8 t}

y = ?

Answer & Explanation

autormtak0w

Beginner2021-12-21Added 31 answers

y^{″} - 10 y^{'} + 17 y = 8 e^{8 t}

r^{2} - 10 r + 17 = 0

r = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 (1) (17)}}{2 (1)}

r = \frac{- (- 10) \pm 4 \sqrt{2}}{2}

r = 5 \pm 2 \sqrt{2}

y_{c} (t) = c_{1} e^{(5 - 2 \sqrt{2}) t} + c_{2} e^{(5 + 2 \sqrt{2}) t}

y_{p} (t) = A e^{8 t}

y_{p}^{'} (t) = 8 A e^{8 t}

y {^{″}}_{p} (t) = 64 A e^{8 t}

y^{″} - 10 y^{'} + 17 y = 8 e^{8 t}

64 A e^{8 t} - 80 A e^{8 t} + 17 A e^{8 t} = 8 e^{8 t}

A e^{8 t} = 8 e^{8 t}

A = 8

y_{p} (t) = 8 e^{8 t}

turtletalk75

Beginner2021-12-22Added 29 answers

What is the point of doing steps 2 and 3 if we don't use them? Also, thank you for the solution!

RizerMix

Expert2021-12-29Added 656 answers

Thanks. Im

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