ODE No. 953

\[ y'(x)=\frac {y(x) \left (x^4 \log ^2(y(x))+2 x^4 \log (x) \log (y(x))+x^4 \log ^2(x)+x^3 \log ^2(y(x))+2 x^3 \log (x) \log (y(x))+x^3 \log ^2(x)+x \log ^2(y(x))+2 x \log (x) \log (y(x))+\log (y(x))+x \log ^2(x)+\log (x)-1\right )}{x} \] Mathematica : cpu = 0.246193 (sec), leaf count = 36

DSolve[Derivative[1][y][x] == ((-1 + Log[x] + x*Log[x]^2 + x^3*Log[x]^2 + x^4*Log[x]^2 + Log[y[x]] + 2*x*Log[x]*Log[y[x]] + 2*x^3*Log[x]*Log[y[x]] + 2*x^4*Log[x]*Log[y[x]] + x*Log[y[x]]^2 + x^3*Log[y[x]]^2 + x^4*Log[y[x]]^2)*y[x])/x,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {e^{-\frac {20 x}{4 x^5+5 x^4+10 x^2+20 c_1}}}{x}\right \}\right \}\] Maple : cpu = 0.371 (sec), leaf count = 145

dsolve(diff(y(x),x) = y(x)*(ln(x)+ln(y(x))-1+x*ln(x)^2+2*x*ln(y(x))*ln(x)+x*ln(y(x))^2+x^3*ln(x)^2+2*x^3*ln(y(x))*ln(x)+x^3*ln(y(x))^2+x^4*ln(x)^2+2*x^4*ln(y(x))*ln(x)+x^4*ln(y(x))^2)/x,y(x))
 

\[y \left (x \right ) = x^{-\frac {4 x^{5}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} x^{-\frac {5 x^{4}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} x^{-\frac {10 x^{2}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} x^{-\frac {20 c_{1}}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}} {\mathrm e}^{-\frac {20 x}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}}\]