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inna [77]
1 year ago
9

Differential equations dy/dx = e^x-y

Mathematics
1 answer:
MA_775_DIABLO [31]1 year ago
5 0

\frac{dy}{dx}=e^{x-y} \\ \\ \frac{dy}{dx}=\frac{e^{x}}{e^{y}} \\ \\ e^{y} \text{ } dy=e^{x} \text{ } dx \\ \\ \int e^{y} \text{ } dy=\int e^{x} \text{ } dx \\ \\ e^{y}=e^{x}+C \\ \\ \boxed{y=\ln \left(e^{x}+C \right)}

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