x^3y^m+2xy^prime-2y=x^2lnx+3x സോൾവ് ചെയ്യുക

$$x ^ { 3 } y ^ { m } + 2 x y ^ { \prime } - 2 y = x ^ { 2 } \ln x + 3 x$$

m എന്നതിനായി സോൾവ് ചെയ്യുക (സങ്കീർണ്ണ സൊല്യൂഷൻ)

$$\left\{\begin{matrix}m=\log_{y}\left(\frac{x^{2}\ln(x)+2y+3x}{x^{3}}\right)+\frac{2\pi n_{1}i}{\ln(y)}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq -\frac{x\left(x\ln(x)+3\right)}{2}\text{ and }y\neq 1\text{ and }y\neq 0\text{ and }x\neq 0\\m\in \mathrm{C}\text{, }&\left(y=0\text{ and }x\left(x\ln(x)+3\right)=0\text{ and }x\neq 0\right)\text{ or }\left(y=1\text{ and }x\left(x\ln(x)-x^{2}+3\right)=-2\text{ and }x\neq 0\right)\end{matrix}\right.$$

m എന്നതിനായി സോൾവ് ചെയ്യുക

$$\left\{\begin{matrix}m=\log_{y}\left(\frac{x^{2}\ln(x)+2y+3x}{x^{3}}\right)\text{, }&y\neq 1\text{ and }y>0\text{ and }y>-\frac{x\left(x\ln(x)+3\right)}{2}\text{ and }x>0\\m\in \mathrm{R}\text{, }&\left(y=-1\text{ and }x\left(x\ln(x)+x^{2}+3\right)=2\text{ and }x>0\text{ and }Denominator(m)\text{bmod}2=1\text{ and }Numerator(m)\text{bmod}2=1\right)\text{ or }\left(y=1\text{ and }x\left(x\ln(x)-x^{2}+3\right)=-2\text{ and }x>0\right)\\m>0\text{, }&y=0\text{ and }x\left(x\ln(x)+3\right)=0\text{ and }x>0\end{matrix}\right.$$