Final answer to the problem
$\ln\left|1-e^y\right|=-x+C_0$
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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
Multiplying polynomials $e^y$ and $\frac{dy}{dx}+1$
Learn how to solve integrals of polynomial functions problems step by step online.
$e^y\frac{dy}{dx}+e^y=1$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation e^y(dy/dx+1)=1. Multiplying polynomials e^y and \frac{dy}{dx}+1. Multiplying the fraction by e^y. We need to isolate the dependent variable y, we can do that by simultaneously subtracting e^y from both sides of the equation. 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
$\ln\left|1-e^y\right|=-x+C_0$
