Final answer to the problem
$\frac{1}{4}\ln\left|\frac{2x^2}{y^2}+1\right|=-\ln\left|y\right|+C_0$
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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
Rewrite the differential equation
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$\left(x^2+y^2\right)\frac{dy}{dx}=-xy$
Learn how to solve problems step by step online. Solve the differential equation (x^2+y^2)dy/dx+xy=0. Rewrite the differential equation. Group terms with common factors. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{-xy}{x^2+y^2} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree.
Final answer to the problem
$\frac{1}{4}\ln\left|\frac{2x^2}{y^2}+1\right|=-\ln\left|y\right|+C_0$
