#### 2.752   ODE No. 752

$y'(x)=\frac {\cos (y(x)) \left (x^3 \cos (y(x))-x-1\right )}{(x+1) (x \sin (y(x))-1)}$ Mathematica : cpu = 28.7776 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == (Cos[y[x]]*(-1 - x + x^3*Cos[y[x]]))/((1 + x)*(-1 + x*Sin[y[x]])), y[x], x]

Maple : cpu = 1.881 (sec), leaf count = 723

$\left \{ y \left ( x \right ) =\arctan \left ( {\frac {1}{36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}+ \left ( -36\,{\it \_C1}+36 \right ) {x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36} \left ( \left ( -2\,{x}^{3}+3\,{x}^{2}+6\,\ln \left ( 1+x \right ) -6\,{\it \_C1}-6\,x \right ) \sqrt {36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}-36\,{\it \_C1}\,{x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36}+36\,x \right ) },{\frac {1}{36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}+ \left ( -36\,{\it \_C1}+36 \right ) {x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36} \left ( 12\,{x}^{4}-18\,{x}^{3}+36\,{x}^{2}+36\,{\it \_C1}\,x-36\,\ln \left ( 1+x \right ) x+6\,\sqrt {36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}-36\,{\it \_C1}\,{x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36} \right ) } \right ) ,y \left ( x \right ) =\arctan \left ( {\frac {1}{36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}+ \left ( -36\,{\it \_C1}+36 \right ) {x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36} \left ( \left ( 2\,{x}^{3}-3\,{x}^{2}+6\,x+6\,{\it \_C1}-6\,\ln \left ( 1+x \right ) \right ) \sqrt {36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}-36\,{\it \_C1}\,{x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36}+36\,x \right ) },{\frac {1}{36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}+ \left ( -36\,{\it \_C1}+36 \right ) {x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36} \left ( 12\,{x}^{4}-18\,{x}^{3}+36\,{x}^{2}+36\,{\it \_C1}\,x-36\,\ln \left ( 1+x \right ) x-6\,\sqrt {36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+ \left ( -24\,{x}^{3}+36\,{x}^{2}-72\,{\it \_C1}-72\,x \right ) \ln \left ( 1+x \right ) +4\,{x}^{6}-12\,{x}^{5}+33\,{x}^{4}+ \left ( 24\,{\it \_C1}-36 \right ) {x}^{3}-36\,{\it \_C1}\,{x}^{2}+72\,{\it \_C1}\,x+36\,{{\it \_C1}}^{2}+36} \right ) } \right ) \right \}$