3.842   ODE No. 842

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)+x^2{(\ln \left(x\right))}^3+2x^2{(\ln \left(x\right))}^{2}y\left(x\right)+x^2\ln \left(x\right){\left(y\left(x\right)\right)}^2}{x\ln \left(x\right)}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.122015 (sec), leaf count = 186 $$\left\{\{y(x)\to -\frac{c_1{e}^{\frac{1}{4}{x}^2(2\log (x)-1)}(\frac{x}{2}+\frac{1}{2}x(2\log (x)-1))+\frac{1}{4}{x}^2{e}^{\frac{1}{4}{x}^2(2\log (x)-1)}(2\log (x)-1)(\frac{x}{2}+\frac{1}{2}x(2\log (x)-1))+\frac{1}{2}x{e}^{\frac{1}{4}{x}^2(2\log (x)-1)}+\frac{1}{2}x{e}^{\frac{1}{4}{x}^2(2\log (x)-1)}(2\log (x)-1)}{x(c_1{e}^{\frac{1}{4}{x}^2(2\log (x)-1)}+\frac{1}{4}{x}^2{e}^{\frac{1}{4}{x}^2(2\log (x)-1)}(2\log (x)-1))}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 43 $$\{y\left(x\right)=-\frac{\ln \left(x\right)(2x^2\ln \left(x\right)-x^2+2\mathit{\_}\mathit{C}\mathit{1}+4)}{2x^2\ln \left(x\right)-x^2+2\mathit{\_}\mathit{C}\mathit{1}}\}$$