What is a solution to the differential equation dy/dx=12x^3y with the particular solution y(0)=2?

Darius Nash 2022-09-13 Answered
What is a solution to the differential equation d y d x = 12 x 3 y with the particular solution y(0)=2?
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Answers (1)

Kenny Kramer
Answered 2022-09-14 Author has 14 answers
This is a separable differential equation, so we can separate the variables and integrate:
d y d x = 12 x 3 y
d y y = 12 x 3 d x
d y y = 12 x 3 d x
ln | y | = 3 x 4 + C 1
y ( x ) = C e 3 x 4
We can now determine the constant C from the initial condition:
y ( 0 ) = 2
2 = C e 0 = C
so in conclusion:
y ( x ) = 2 e 3 x 4

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