Final answer to the problem
$\frac{y}{-x}=\ln\left|y\right|+C_0$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^2dx=(x^2+xy)dy. We can identify that the differential equation y^2dx=\left(x^2+xy\right)dy 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: x=uy. Expand and simplify. Group the terms of the differential equation. Move the terms of the u variable to the left side, and the terms of the y variable to the right side of the equality.
Final answer to the problem
$\frac{y}{-x}=\ln\left|y\right|+C_0$
