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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 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. Rewrite the differential equation. 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.