Solve the equation y′ + 3y = t + e^ (-2t).

Question

Kibbles

Mathematics

17 October, 16:00

Solve the equation y′ + 3y = t + e^ (-2t).

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Vinnie · Answer 1

Hello,

I am going to remember:

y'+3y=0==>y=C*e^ (-3t)

y'=C'*e^ (-3t) - 3C*e^ (-3t)

y'+3y=C'*e^ (-3t) - 3Ce^ (-3t) + 3C*e^ (-3t) = C'*e^ (-3t) = t+e^ (-2t)

==>C' = (t+e^ (-2t)) / e^ (-3t) = t*e^ (3t) + e^t

==>C=e^t+t*e^ (3t) / 3-e^ (3t) / 9

==>y = (e^t+t*e^ (3t) / 3-e^ (3t) / 9) * e^ (-3t) + D

==>y=e^ (-2t) + t/3-1/9+D

==>y=e^ (-2t) + t/3+k