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Rewrite the differential equation using Leibniz notation
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$x\frac{dy}{dx}+y\ln\left(x\right)=y\ln\left(y\right)+y$
Learn how to solve differential equations problems step by step online. Solve the differential equation xy^'+yln(x)=yln(y)+y. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable , we can do that by simultaneously subtracting y\ln\left(x\right) from both sides of the equation. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y\ln\left(y\right)+y-y\ln\left(x\right)}{x} 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.