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 = 0.073791 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [c_1 \log (\text {$\#$1})-\cos (\text {$\#$1})\& \right ]\left [c_2+x\right ]\right \}\right \}\]
Maple ✓
cpu = 0.119 (sec), leaf count = 24
\[ \left \{ -\cos \left ( y \left ( x \right ) \right ) +{\it \_C1}\,\ln \left ( y \left ( x \right ) \right ) -x-{\it \_C2}=0,y \left ( x \right ) ={\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1, -cos(y(x))+_C1*ln(y(x))-x-_C2 = 0