ODE
\[ y(x) y''(x)=-x^2 y(x)^2+y'(x)^2+y(x)^2 \log (y(x)) \] ODE Classification
[[_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.396126 (sec), leaf count = 30
\[\left \{\left \{y(x)\to e^{x^2-\frac {c_1 e^x}{2}-c_2 e^{-x}+2}\right \}\right \}\]
Maple ✓
cpu = 1.315 (sec), leaf count = 27
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {{\mathrm e}^{-2 x} \textit {\_C1} \,{\mathrm e}^{x}}{2}} {\mathrm e}^{-\frac {\textit {\_C2} \,{\mathrm e}^{x}}{2}} {\mathrm e}^{x^{2}} {\mathrm e}^{2}\right ]\] Mathematica raw input
DSolve[y[x]*y''[x] == -(x^2*y[x]^2) + Log[y[x]]*y[x]^2 + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> E^(2 + x^2 - (E^x*C[1])/2 - C[2]/E^x)}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+y(x)^2*ln(y(x))-x^2*y(x)^2, y(x))
Maple raw output
[y(x) = exp(1/2*exp(-2*x)*_C1*exp(x))*exp(-1/2*_C2*exp(x))*exp(x^2)*exp(2)]