\[ y'(x)^2 (a \cos (y(x))+b)-c \cos (y(x))+d=0 \] ✓ Mathematica : cpu = 7.0104 (sec), leaf count = 605
DSolve[d - c*Cos[y[x]] + (b + a*Cos[y[x]])*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {4 \sin ^2\left (\frac {\text {$\#$1}}{2}\right ) \csc (\text {$\#$1}) \sqrt {a \cos (\text {$\#$1})+b} \sqrt {\frac {\cot ^2\left (\frac {\text {$\#$1}}{2}\right ) (c-d)}{c+d}} \sqrt {\frac {\csc ^2\left (\frac {\text {$\#$1}}{2}\right ) (a+b) (d-c \cos (\text {$\#$1}))}{a d+b c}} \left (c (a+b) \operatorname {EllipticF}\left (\arcsin \left (\frac {\sqrt {\frac {(a+b) (d-c \cos (\text {$\#$1})) \csc ^2\left (\frac {\text {$\#$1}}{2}\right )}{b c+a d}}}{\sqrt {2}}\right ),\frac {2 (b c+a d)}{(a+b) (c+d)}\right )+a (d-c) \operatorname {EllipticPi}\left (\frac {b c+a d}{a c+b c},\arcsin \left (\frac {\sqrt {\frac {(a+b) (d-c \cos (\text {$\#$1})) \csc ^2\left (\frac {\text {$\#$1}}{2}\right )}{b c+a d}}}{\sqrt {2}}\right ),\frac {2 (b c+a d)}{(a+b) (c+d)}\right )\right )}{c (a+b) \sqrt {c \cos (\text {$\#$1})-d} \sqrt {\frac {\csc ^2\left (\frac {\text {$\#$1}}{2}\right ) (c-d) (a \cos (\text {$\#$1})+b)}{a d+b c}}}\& \right ][-x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {4 \sin ^2\left (\frac {\text {$\#$1}}{2}\right ) \csc (\text {$\#$1}) \sqrt {a \cos (\text {$\#$1})+b} \sqrt {\frac {\cot ^2\left (\frac {\text {$\#$1}}{2}\right ) (c-d)}{c+d}} \sqrt {\frac {\csc ^2\left (\frac {\text {$\#$1}}{2}\right ) (a+b) (d-c \cos (\text {$\#$1}))}{a d+b c}} \left (c (a+b) \operatorname {EllipticF}\left (\arcsin \left (\frac {\sqrt {\frac {(a+b) (d-c \cos (\text {$\#$1})) \csc ^2\left (\frac {\text {$\#$1}}{2}\right )}{b c+a d}}}{\sqrt {2}}\right ),\frac {2 (b c+a d)}{(a+b) (c+d)}\right )+a (d-c) \operatorname {EllipticPi}\left (\frac {b c+a d}{a c+b c},\arcsin \left (\frac {\sqrt {\frac {(a+b) (d-c \cos (\text {$\#$1})) \csc ^2\left (\frac {\text {$\#$1}}{2}\right )}{b c+a d}}}{\sqrt {2}}\right ),\frac {2 (b c+a d)}{(a+b) (c+d)}\right )\right )}{c (a+b) \sqrt {c \cos (\text {$\#$1})-d} \sqrt {\frac {\csc ^2\left (\frac {\text {$\#$1}}{2}\right ) (c-d) (a \cos (\text {$\#$1})+b)}{a d+b c}}}\& \right ][x+c_1]\right \}\right \}\] ✓ Maple : cpu = 6.255 (sec), leaf count = 87
dsolve(diff(y(x),x)^2*(a*cos(y(x))+b)-c*cos(y(x))+d=0,y(x))
\[y \left (x \right ) = \arccos \left (\frac {d}{c}\right )\]