2.194   ODE No. 194

\[ x \log (x) y'(x)-y(x) \left (2 \log ^2(x)+1\right )-y(x)^2 \log (x)-\log ^3(x)=0 \]

✓ Mathematica : cpu = 0.127044 (sec), leaf count = 98

DSolve[-Log[x]^3 - (1 + 2*Log[x]^2)*y[x] - Log[x]*y[x]^2 + x*Log[x]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {x \left (\frac {e^{\frac {\log ^2(x)}{2}} \log (x)}{x}+\frac {e^{\frac {\log ^2(x)}{2}} \log ^3(x)}{2 x}+\frac {c_1 e^{\frac {\log ^2(x)}{2}} \log (x)}{x}\right )}{\frac {1}{2} e^{\frac {\log ^2(x)}{2}} \log ^2(x)+c_1 e^{\frac {\log ^2(x)}{2}}}\right \}\right \}\]

✓ Maple : cpu = 0.027 (sec), leaf count = 23

dsolve(x*diff(y(x),x)*ln(x)-y(x)^2*ln(x)-(2*ln(x)^2+1)*y(x)-ln(x)^3 = 0,y(x))
 

\[y \left (x \right ) = -\frac {\ln \left (x \right ) \left (\ln \left (x \right )^{2}+c_{1} +2\right )}{\ln \left (x \right )^{2}+c_{1}}\]