2.357   ODE No. 357

\[ x \log (x) y'(x) \sin (y(x))+\cos (y(x)) (1-x \cos (y(x)))=0 \] Mathematica : cpu = 0.39176 (sec), leaf count = 35

DSolve[Cos[y[x]]*(1 - x*Cos[y[x]]) + x*Log[x]*Sin[y[x]]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\sec ^{-1}\left (\frac {x-c_1}{\log (x)}\right )\right \},\left \{y(x)\to \sec ^{-1}\left (\frac {x-c_1}{\log (x)}\right )\right \}\right \}\] Maple : cpu = 0.467 (sec), leaf count = 13

dsolve(x*diff(y(x),x)*ln(x)*sin(y(x))+cos(y(x))*(1-x*cos(y(x))) = 0,y(x))
 

\[y \left (x \right ) = \operatorname {arcsec}\left (\frac {x +c_{1}}{\ln \left (x \right )}\right )\]