Final answer to the problem
$-\frac{1}{2}\ln\left|\frac{x}{y}\right|+\frac{-x}{2y}=\ln\left|y\right|+C_0$
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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
Expand the fraction $\frac{x+y}{x}$ into $2$ simpler fractions with common denominator $x$
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$\frac{dy}{dx}\frac{x-y}{y}=\frac{x}{x}+\frac{y}{x}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx(x-y)/y=(x+y)/x. Expand the fraction \frac{x+y}{x} into 2 simpler fractions with common denominator x. Simplify the resulting fractions. Rewrite the differential equation. Combine 1+\frac{y}{x} in a single fraction.
Final answer to the problem
$-\frac{1}{2}\ln\left|\frac{x}{y}\right|+\frac{-x}{2y}=\ln\left|y\right|+C_0$
