Find-constant-a-b-so-that-y-t-t-3-e-2t-is-solution-of-IVP-y-ay-e-2t-y-0-b-

Question Number 182139 by Mastermind last updated on 04/Dec/22

Find constant a, b, so that

y (t) = (t + 3) e^{2 t} is solution of IVP

y^{^{'}} = ay + e^{2 t}, y (0) = b

.

Commented by mr W last updated on 06/Dec/22

d o y o u n e v e r g i v e a f e e d b a c k w h e n a

q u e s t i o n o f y o u r s i s a n s w e r e d ?

Answered by mr W last updated on 04/Dec/22

y^{'} = e^{2 t} + 2 (t + 3) e^{2 t}

e^{2 t} + 2 (t + 3) e^{2 t} = a (t + 3) e^{2 t} + e^{2 t}

\Rightarrow 2 = a

y (0) = (0 + 3) e^{0} = 3 = b

Commented by Mastermind last updated on 22/Dec/22

Thank you boss