\[ A y(x) \left (a \sin ^2(y(x))+c\right )+y''(x) \left (a \sin ^2(y(x))+b\right )+a y'(x)^2 \sin (y(x)) \cos (y(x))=0 \] ✗ Mathematica : cpu = 103.045 (sec), leaf count = 0 , could not solve
DSolve[A*(c + a*Sin[y[x]]^2)*y[x] + a*Cos[y[x]]*Sin[y[x]]*Derivative[1][y][x]^2 + (b + a*Sin[y[x]]^2)*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.421 (sec), leaf count = 138
\[ \left \{ \int ^{y \left ( x \right ) }\!{\sqrt {2} \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) {\frac {1}{\sqrt {- \left ( a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2}A-2\,a{\it \_a}\,\cos \left ( {\it \_a} \right ) \sin \left ( {\it \_a} \right ) A+{{\it \_a}}^{2} \left ( a+2\,c \right ) A-2\,{\it \_C1} \right ) \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\sqrt {2} \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) {\frac {1}{\sqrt {- \left ( a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2}A-2\,a{\it \_a}\,\cos \left ( {\it \_a} \right ) \sin \left ( {\it \_a} \right ) A+{{\it \_a}}^{2} \left ( a+2\,c \right ) A-2\,{\it \_C1} \right ) \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]