Simplify. x(dy/dx) - 3y - x^6 e^(x^3) , y(0) = 2

Leila Jennings 2022-08-01 Answered
Simplify. x ( d y / d x ) 3 y x 6 e x 3 , y ( 0 ) = 2
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Answers (1)

Jazlene Dickson
Answered 2022-08-02 Author has 15 answers
d y d x 3 y x = x 5 e x 3 linear diff. eqn.
y' +P(x) y = Q(x)
P(x)=-3/y
Q ( x ) = x 5 exp ( x 3 )
i ( x ) = exp ( 3 x d x ) = exp ( 3 ln x ) = exp ( ln x 3 ) = 1 x 3
y = 1 x 3 x 5 e x 3 d x + c
y = x 2 e x 3 d x + c
x 3 = u
3 x 2 d x = d u
x 2 d x = d u / 3
y = 1 3 e u d u + c
y = e x 3 3 + c
y = x 3 e x 3 3 + c x 3
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