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We can identify that the differential equation $x\cdot dx+\left(y-2x\right)dy=0$ 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
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$x\cdot dx+\left(y-2x\right)dy=0$
Learn how to solve problems step by step online. xdx+(y-2x)dy=0. We can identify that the differential equation x\cdot dx+\left(y-2x\right)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: x=uy. Expand and simplify. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=\frac{1}{y}, b=\frac{u}{-\left(u-1\right)^{2}}, dx=dy, dy=du, dyb=dxa=\frac{u}{-\left(u-1\right)^{2}}du=\frac{1}{y}dy, dyb=\frac{u}{-\left(u-1\right)^{2}}du and dxa=\frac{1}{y}dy.
