\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a\sin \left ( \alpha \,y \left ( x \right ) +\beta \,x \right ) +b=0} \]
Mathematica: cpu = 0.860609 (sec), leaf count = 1317 \[ \left \{\left \{y(x)\to \frac {2 \tan ^{-1}\left (\frac {\frac {a^2 \sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )} \tan \left (\frac {1}{2} \left (\frac {a^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {b^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {a^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {b^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {2 b \beta x \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {2 b \beta c_1 \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {\beta ^2 x}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {\beta ^2 c_1}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}\right )\right ) \alpha ^2}{(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}-\frac {b^2 \sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )} \tan \left (\frac {1}{2} \left (\frac {a^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {b^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {a^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {b^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {2 b \beta x \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {2 b \beta c_1 \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {\beta ^2 x}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {\beta ^2 c_1}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}\right )\right ) \alpha ^2}{(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}-a \alpha +\frac {2 b \beta \sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )} \tan \left (\frac {1}{2} \left (\frac {a^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {b^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {a^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {b^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {2 b \beta x \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {2 b \beta c_1 \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {\beta ^2 x}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {\beta ^2 c_1}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}\right )\right ) \alpha }{(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}-\frac {\beta ^2 \sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )} \tan \left (\frac {1}{2} \left (\frac {a^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {b^2 x \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {a^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {b^2 c_1 \alpha ^2}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {2 b \beta x \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {2 b \beta c_1 \alpha }{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}-\frac {\beta ^2 x}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}+\frac {\beta ^2 c_1}{\sqrt {-(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}\right )\right )}{(a \alpha +b \alpha -\beta ) (a \alpha -b \alpha +\beta )}}{\alpha b-\beta }\right )-\beta x}{\alpha }\right \}\right \} \]
Maple: cpu = 0.655 (sec), leaf count = 118 \[ \left \{ y \left ( x \right ) ={\frac {1}{\alpha } \left ( -\beta \,x+2\, \arctan \left ( {\frac {\tan \left ( 1/2\,{\it \_C1}\,\sqrt {-{a}^{2}{ \alpha }^{2}+{\alpha }^{2}{b}^{2}-2\,\alpha \,b\beta +{\beta }^{2}}-1/2\,x \sqrt {-{a}^{2}{\alpha }^{2}+{\alpha }^{2}{b}^{2}-2\,\alpha \,b\beta +{ \beta }^{2}} \right ) \sqrt {-{a}^{2}{\alpha }^{2}+{\alpha }^{2}{b}^{2}-2 \,\alpha \,b\beta +{\beta }^{2}}-a\alpha }{b\alpha -\beta }} \right ) \right ) } \right \} \]