What is a solution to the differential equation dydx=ex−y?

Explanation:dydx=ex−y=ex⋅e−y we can separate it!eydydx=ex∫eydydxdx=∫exdx∫eydy=∫exdxey=ex+Cln⁡(ey)=ln⁡(ex+C)y=ln⁡(ex+C)

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Cash Duncan

2022-04-18

What is a solution to the differential equation

\frac{d y}{d x} = e^{x - y}

abangan85s0

Beginner2022-04-19Added 16 answers

Explanation:

\frac{d y}{d x} = e^{x - y}

= e^{x} \cdot e^{- y}

we can separate it!

e^{y} \frac{d y}{d x} = e^{x}

\int e^{y} \frac{d y}{d x} d x = \int e^{x} d x

\int e^{y} d y = \int e^{x} d x

e^{y} = e^{x} + C

\ln (e^{y}) = \ln (e^{x} + C)

y = \ln (e^{x} + C)

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