How do you solve for the equation

Malik Dean

Malik Dean

Answered question

2022-04-10

How do you solve for the equation dydx=3x2e2y that satisfies the initial condition f(0)=12?

Answer & Explanation

ysnlm8eut

ysnlm8eut

Beginner2022-04-11Added 14 answers

First of all, I think ther is a mistake in your writing, I think you wanted to write:
dydx=3x2e2y
This is a separable differential equations, so:
e2ydy=3x2dxe2ydy=3x2dx
12e2y=x3+c
Now to find c let's use the condition: f(0)=12e.
So the solution is:
12e2y=x3+12ee2y=2x3+e2y=ln(2x3+e)
y=12ln(2x3+e)

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