Final answer to the problem
$y=\ln\left|x+1\right|+C_0$
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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
Rewrite the differential equation using Leibniz notation
$x\frac{dy}{dx}=1-\frac{dy}{dx}$
Learn how to solve differential equations problems step by step online.
$x\frac{dy}{dx}=1-\frac{dy}{dx}$
Learn how to solve differential equations problems step by step online. Solve the differential equation xy^'=1-y^'. Rewrite the differential equation using Leibniz notation. Rewrite the differential equation. Combine 1+\frac{-dy}{dx} in a single fraction. Divide fractions \frac{\frac{-dy+dx}{dx}}{x} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
Final answer to the problem
$y=\ln\left|x+1\right|+C_0$
