ODE
\[ y(x) y''(x)=y'(x)^2 \left (y'(x) (-\sin (y(x)))-y(x) y'(x) \cos (y(x))+1\right ) \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.399789 (sec), leaf count = 23
\[\{\{y(x)\to \text {InverseFunction}[-\cos (\text {$\#$1})+c_1 \log (\text {$\#$1})\& ][x+c_2]\}\}\]
Maple ✓
cpu = 2.432 (sec), leaf count = 24
\[[y \left (x \right ) = \textit {\_C1}, -\cos \left (y \left (x \right )\right )+\textit {\_C1} \ln \left (y \left (x \right )\right )-x -\textit {\_C2} = 0]\] Mathematica raw input
DSolve[y[x]*y''[x] == y'[x]^2*(1 - Sin[y[x]]*y'[x] - Cos[y[x]]*y[x]*y'[x]),y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[-Cos[#1] + C[1]*Log[#1] & ][x + C[2]]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2*(1-diff(y(x),x)*sin(y(x))-y(x)*diff(y(x),x)*cos(y(x))), y(x))
Maple raw output
[y(x) = _C1, -cos(y(x))+_C1*ln(y(x))-x-_C2 = 0]