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- Exact Differential Equation
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Multiplying polynomials $y$ and $\ln\left|y\right|-\ln\left|x\right|+1$
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$\frac{dy}{dx}=\frac{y\ln\left|y\right|+y\left(-\ln\left|x\right|+1\right)}{x}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(y(ln(y)-ln(x)+1))/x. Multiplying polynomials y and \ln\left|y\right|-\ln\left|x\right|+1. Multiplying polynomials y and -\ln\left|x\right|+1. Any expression multiplied by 1 is equal to itself. We can identify that the differential equation \frac{dy}{dx}=\frac{y\ln\left(y\right)-y\ln\left(x\right)+y}{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.
