\[ A y(x) \left (a \sin ^2(y(x))+c\right )+y''(x) \left (a \sin ^2(y(x))+b\right )+a y'(x)^2 \sin (y(x)) \cos (y(x))=0 \] ✓ Mathematica : cpu = 26.4505 (sec), leaf count = 176
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {\sqrt {2} \sqrt {\cos (2 K[1]) a-a-2 b}}{\sqrt {2 a A K[1]^2+4 A c K[1]^2-2 a A \sin (2 K[1]) K[1]+2 c_1-a A \cos (2 K[1])}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt {2} \sqrt {\cos (2 K[2]) a-a-2 b}}{\sqrt {2 a A K[2]^2+4 A c K[2]^2-2 a A \sin (2 K[2]) K[2]+2 c_1-a A \cos (2 K[2])}}dK[2]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.944 (sec), leaf count = 138
\[ \left \{ \int ^{y \left ( x \right ) }\!{\sqrt {2} \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) {\frac {1}{\sqrt {- \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) \left ( Aa \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2}-2\,Aa{\it \_a}\,\cos \left ( {\it \_a} \right ) \sin \left ( {\it \_a} \right ) +{{\it \_a}}^{2} \left ( a+2\,c \right ) A-2\,{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\sqrt {2} \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) {\frac {1}{\sqrt {- \left ( b+a \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2} \right ) \left ( Aa \left ( \sin \left ( {\it \_a} \right ) \right ) ^{2}-2\,Aa{\it \_a}\,\cos \left ( {\it \_a} \right ) \sin \left ( {\it \_a} \right ) +{{\it \_a}}^{2} \left ( a+2\,c \right ) A-2\,{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]