What is a solution to the differential equation \frac{dy}{dx}=\frac{2x}{e^{2y}}?

Harrison Reeves

Harrison Reeves

Answered question

2022-04-19

What is a solution to the differential equation dydx=2xe2y?

Answer & Explanation

abangan85s0

abangan85s0

Beginner2022-04-20Added 16 answers

This is a separable differential equation.
dy(e2y)=2xdx
(dye2y)=(2xdx)
12e2y=x2
It is often preferable to solve for y.
e2y=x212
e2y=2x2
ln(e2y)=ln(2x2)
2ylne=ln(2x2)
2y=ln(2x2)
y=12ln(2x2)
y=ln2x2

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