解決(y/x^2+2)dx+1/x[1+ln(xy)]dy=0 |Microsoft數學求解器

$$( \frac { y } { x ^ { 2 } } + 2 ) d x + \frac { 1 } { x } [ 1 + \ln ( x y ) ] d y = 0$$

解 d (復數求解)

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\text{ and }x\neq 0\\d\in \mathrm{C}\text{, }&y\neq 0\text{ and }x\neq 0\text{ and }y\ln(xy)+2x^{2}=-2y\end{matrix}\right.$$

解 d

$$\left\{\begin{matrix}d=0\text{, }&\left(x<0\text{ and }y<0\right)\text{ or }\left(x>0\text{ and }y>0\right)\\d\in \mathrm{R}\text{, }&x\neq 0\text{ and }\left(x<0\text{ or }y>0\right)\text{ and }\left(y<0\text{ or }x>0\right)\text{ and }y\neq 0\text{ and }y\ln(xy)+2x^{2}=-2y\end{matrix}\right.$$