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Rewrite the differential equation using Leibniz notation
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$x\frac{dy}{dx}+y\left(\ln\left(x\right)-\ln\left(y\right)-1\right)=0$
Learn how to solve problems step by step online. Solve the differential equation xy^'+y(ln(x)-ln(y)+-1)=0. Rewrite the differential equation using Leibniz notation. Solve the product y\left(\ln\left(x\right)-\ln\left(y\right)-1\right). Solve the product y\left(-\ln\left(y\right)-1\right). We can identify that the differential equation x\frac{dy}{dx}+y\ln\left(x\right)-y\ln\left(y\right)-y=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.