What is a solution to the differential equation \frac{dy}{dx}=12x^{3}y with

Emmy Decker

Emmy Decker

Answered question

2022-04-16

What is a solution to the differential equation dydx=12x3y with the particular solution y(0)=2?

Answer & Explanation

Nico Buck

Nico Buck

Beginner2022-04-17Added 9 answers

This is a separable differential equation, so we can separate the variables and integrate:
dydx=12x3y
dyy=12x3dx
dyy=12x3dx
ln|y|=3x4+C1
y(x)=Ce3x4
We can now determine the constant C from the initial condition:
y(0)=2
2=Ce0=C
so in conclusion:
y(x)=2e3x4

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