Final answer to the problem
$\ln\left|\frac{y}{x}+1\right|+\frac{x}{y+x}=-\ln\left|x\right|+C_0$
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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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$\left(x+2y\right)dx+y\cdot dy=0$
Learn how to solve problems step by step online. Solve the differential equation (x+2y)dx+ydy=0. We can identify that the differential equation \left(x+2y\right)dx+y\cdot dy=0 is homogeneous, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, 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. Use the substitution: y=ux. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to x.
Final answer to the problem
$\ln\left|\frac{y}{x}+1\right|+\frac{x}{y+x}=-\ln\left|x\right|+C_0$
