2.924   ODE No. 924

\[ y'(x)=\frac {y(x) \left (\text {$\_$F1}(x)+\frac {\log ^2(y(x))}{2 x}\right )}{\log (y(x))} \]

✓ Mathematica : cpu = 0.237304 (sec), leaf count = 80

DSolve[Derivative[1][y][x] == (y[x]*(Log[y[x]]^2/(2*x) + _F1[x]))/Log[y[x]],y[x],x]
 

\[\text {Solve}\left [\int _1^x\left (-\frac {\log ^2(y(x))}{2 K[1]^2}-\frac {\text {$\_$F1}(K[1])}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (\frac {\log (K[2])}{x K[2]}-\int _1^x-\frac {\log (K[2])}{K[1]^2 K[2]}dK[1]\right )dK[2]=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.185 (sec), leaf count = 46

dsolve(diff(y(x),x) = -(-1/2*ln(y(x))^2/x-_F1(x))/ln(y(x))*y(x),y(x))
 

\[y \left (x \right ) = {\mathrm e}^{\sqrt {2}\, \sqrt {x \left (\int \frac {\textit {\_F1} \left (x \right )}{x}d x +c_{1} \right )}}\]