Final answer to the problem
$-\ln\left|\frac{y}{x}+1\right|-\ln\left|\frac{-y}{x}+1\right|=\ln\left|x\right|+C_0$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
- Load more...
Can't find a method? Tell us so we can add it.
1
Grouping the terms of the differential equation
Learn how to solve problems step by step online.
$2y\cdot dy=\frac{x^2+y^2}{x}dx$
Learn how to solve problems step by step online. Solve the differential equation 2xydy=(x^2+y^2)dx. Grouping the terms of the differential equation. Divide both sides of the equation by dx. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{x^2+y^2}{2xy} 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
$-\ln\left|\frac{y}{x}+1\right|-\ln\left|\frac{-y}{x}+1\right|=\ln\left|x\right|+C_0$
