Final answer to the problem
$y=\left(-\ln\left(x\right)+C_0\right)x$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation (x-y)dx+xdy=0. We can identify that the differential equation \left(x-y\right)dx+x\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. Simplify the expression {0}.
Final answer to the problem
$y=\left(-\ln\left(x\right)+C_0\right)x$
