What is the general solution of the differential equation? : dy/dx+3y=3x^2e^(−3x)

Liam Keller 2022-09-13 Answered
What is the general solution of the differential equation? : d y d x + 3 y = 3 x 2 e - 3 x
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Answers (1)

Dalton Erickson
Answered 2022-09-14 Author has 10 answers
d y d x + 3 y = 3 x 2 e - 3 x
d y d x e 3 x + 3 y e 3 x = 3 x 2 e - 3 x e 3 x
d d x ( y e 3 x ) = 3 x 2
y e 3 x = x 3 + C
y = ( x 3 + C ) e - 3 x
Note: This differential equation is first order and linear one.
1) I multiplied both sides with e 3 x for converting left side to the exact differential equation.
2) I integrated both sides.
3) I multiplied with e - 3 x for solving y.

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