Final answer to the problem
$-\frac{1}{2}\ln\left(\frac{y}{x}+1\right)+\frac{1}{2}\ln\left(\frac{y}{x}-1\right)=\ln\left(x\right)+C_0$
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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
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$x^2\frac{dy}{dx}-xy=y^2-x^2$
Learn how to solve problems step by step online. Solve the differential equation x^2y^'-xy=y^2-x^2. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -xy from both sides of the equation. Multiply -1 times -1. Rewrite the differential equation.
Final answer to the problem
$-\frac{1}{2}\ln\left(\frac{y}{x}+1\right)+\frac{1}{2}\ln\left(\frac{y}{x}-1\right)=\ln\left(x\right)+C_0$
