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

Ansley Sparks

Ansley Sparks

Answered question

2022-04-16

What is a solution to the differential equation dydx=2exy with the initial condition y(1)=ln(2e+1)?

Answer & Explanation

phoenixtreeaung

phoenixtreeaung

Beginner2022-04-17Added 19 answers

Explanation:
this is separable
dydx=2exy=2exey
So
eydydx=2ex
eydydxdx=2exdx
ddx(ey)dx=2exdx
ey=2ex+C
y=ln(2ex+C)
y(1)=ln(2e+1)
ln(2e+1)=ln(2e+C)C=1
y=ln(2ex+1)

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