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We can identify that the differential equation $\left(2y-3x\right)dx+x\cdot dy=0$ 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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$\left(2y-3x\right)dx+x\cdot dy=0$
Learn how to solve problems step by step online. (2y-3x)dx+xdy=0. We can identify that the differential equation \left(2y-3x\right)dx+x\cdot 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: y=ux. Expand and simplify. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=\frac{3}{x}, b=\frac{1}{-u+1}, dy=du, dyb=dxa=\frac{1}{-u+1}du=\frac{3}{x}dx, dyb=\frac{1}{-u+1}du and dxa=\frac{3}{x}dx.
