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- Equazione differenziale esatta
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We can identify that the differential equation $\frac{dy}{dx}=\frac{y-x}{x}$ 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
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$\frac{dy}{dx}=\frac{y-x}{x}$
Learn how to solve problems step by step online. dy/dx=(y-x)/x. We can identify that the differential equation \frac{dy}{dx}=\frac{y-x}{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. Use the substitution: y=ux. Expand and simplify. Apply the formula: dy=a\cdot dx\to \int1dy=\int adx, where a=\frac{-1}{x}.
