Final answer to the problem
$\ln\left|\frac{1}{e^y}+1\right|+y=e^x+x+C_0$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$
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$\frac{dy}{dx}=e^xe^{-y}+e^x+e^{-y}+1$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=e^(x-y)+e^xe^(-y)+1. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Factoring by e^x. Factoring by 1+e^{-y}. 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.
Final answer to the problem
$\ln\left|\frac{1}{e^y}+1\right|+y=e^x+x+C_0$
