ODE No. 957

3.957 ODE No. 957

$\frac{d}{d x} y (x) = \frac{y (x)}{(\ln (x) + 1) x} (- 1 - x^{3} x^{2 {(\ln (x) + 1)}^{- 1}} e^{2 \frac{{(\ln (x))}^{2}}{\ln (x) + 1}} - x^{3} x^{2 {(\ln (x) + 1)}^{- 1}} e^{2 \frac{{(\ln (x))}^{2}}{\ln (x) + 1}} \ln (x) + x^{3} x^{2 {(\ln (x) + 1)}^{- 1}} e^{2 \frac{{(\ln (x))}^{2}}{\ln (x) + 1}} y (x) + 2 x^{3} x^{2 {(\ln (x) + 1)}^{- 1}} e^{2 \frac{{(\ln (x))}^{2}}{\ln (x) + 1}} y (x) \ln (x) + x^{3} x^{2 {(\ln (x) + 1)}^{- 1}} e^{2 \frac{{(\ln (x))}^{2}}{\ln (x) + 1}} y (x) {(\ln (x))}^{2}) = 0$

Mathematica: cpu = 0.198525 (sec), leaf count = 28 ${{y (x) \to \frac{1}{(c_{1} e^{\frac{x^{5}}{5}} + 1) (\log (x) + 1)}}}$

Maple: cpu = 0.031 (sec), leaf count = 197 ${y (x) = 1 e^{- \frac{x^{5}}{5}} {({(\ln (x))}^{2} e^{\frac{- x^{5} \ln (x) - x^{5} + 10 {(\ln (x))}^{2} - 5 \ln (\ln (x) + 1) \ln (x) - 5 \ln (\ln (x) + 1)}{5 \ln (x) + 5}} x^{- 2 \frac{\ln (x)}{\ln (x) + 1}} + 2 \ln (x) e^{1 / 5 \frac{- x^{5} \ln (x) - x^{5} + 10 {(\ln (x))}^{2} - 5 \ln (\ln (x) + 1) \ln (x) - 5 \ln (\ln (x) + 1)}{\ln (x) + 1}} x^{- 2 \frac{\ln (x)}{\ln (x) + 1}} +_C 1 \ln (x) + e^{\frac{- x^{5} \ln (x) - x^{5} + 10 {(\ln (x))}^{2} - 5 \ln (\ln (x) + 1) \ln (x) - 5 \ln (\ln (x) + 1)}{5 \ln (x) + 5}} x^{- 2 \frac{\ln (x)}{\ln (x) + 1}} +_C 1)}^{- 1}}$

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