ODE
\[ a y'(x)^2+b \sin (y(x))+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 100.106 (sec), leaf count = 0 , could not solve
DSolve[b*Sin[y[x]] + a*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.173 (sec), leaf count = 115
\[ \left \{ \int ^{y \left ( x \right ) }\!{(-4\,{a}^{2}-1){\frac {1}{\sqrt {16\,{\it \_C1}\, \left ( {a}^{2}+1/4 \right ) ^{2}{{\rm e}^{-2\,{\it \_a}\,a}}-16\, \left ( a\sin \left ( {\it \_a} \right ) -1/2\,\cos \left ( {\it \_a} \right ) \right ) \left ( {a}^{2}+1/4 \right ) b}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{(4\,{a}^{2}+1){\frac {1}{\sqrt {16\,{\it \_C1}\, \left ( {a}^{2}+1/4 \right ) ^{2}{{\rm e}^{-2\,{\it \_a}\,a}}-16\, \left ( a\sin \left ( {\it \_a} \right ) -1/2\,\cos \left ( {\it \_a} \right ) \right ) \left ( {a}^{2}+1/4 \right ) b}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[b*Sin[y[x]] + a*y'[x]^2 + y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[b*Sin[y[x]] + a*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)^2+b*sin(y(x)) = 0, y(x),'implicit')
Maple raw output
Intat((4*a^2+1)/(16*_C1*(a^2+1/4)^2*exp(-2*_a*a)-16*(a*sin(_a)-1/2*cos(_a))*(a^2+1/4)*b)^(1/2),_a = y(x))-x-_C2 = 0, Intat((-4*a^2-1)/(16*_C1*(a^2+1/4)^2*exp(-2*_a*a)-16*(a*sin(_a)-1/2*cos(_a))*(a^2+1/4)*b)^(1/2),_a = y(x))-x-_C2 = 0