3.963   ODE No. 963

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/4\,{\frac {-4\,\cos \left ( x \right ) x+4\,{x}^{2}\sin \left ( x \right ) +4\,x+4+4\, \left ( y \left ( x \right ) \right ) ^{2}+8\,y \left ( x \right ) \cos \left ( x \right ) x-8\,xy \left ( x \right ) +2\,{x}^{2}\cos \left ( 2\,x \right ) +6\,{x}^{2}-8\,{x}^{2}\cos \left ( x \right ) +4\, \left ( y \left ( x \right ) \right ) ^{3}+12\, \left ( y \left ( x \right ) \right ) ^{2}\cos \left ( x \right ) x-12\,x \left ( y \left ( x \right ) \right ) ^{2}+6\,y \left ( x \right ) {x}^{2}\cos \left ( 2\,x \right ) +18\,{x}^{2}y \left ( x \right ) -24\,y \left ( x \right ) \cos \left ( x \right ) {x}^{2}+{x}^{3}\cos \left ( 3\,x \right ) +15\,{x}^{3}\cos \left ( x \right ) -6\,{x}^{3}\cos \left ( 2\,x \right ) -10\,{x}^{3}}{x}}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.112014 (sec), leaf count = 108 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 y(x)}{x}+\frac {-3 x+3 x \cos (x)+1}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x),y(x)\right ] \]

Maple: cpu = 0.156 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =-\cos \left ( x \right ) x+x-{\frac {1}{3}} +{\frac {29\,{\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\, {{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( x \right ) +3\,{\it \_C1} \right ) }{9}} \right \} \]