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The quotient of powers of same base ($\frac{e^x}{e^y}$) can be rewritten as the base to the power of the difference of the exponents
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$\frac{dy}{dx}\left(1+e^x\right)=e^{\left(x-y\right)}$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx(1+e^x)=(e^x)/(e^y). The quotient of powers of same base (\frac{e^x}{e^y}) can be rewritten as the base to the power of the difference of the exponents. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to .