2.950   ODE No. 950

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

\[ y'(x)=\frac {3}{32} a^2 b x^5+\frac {3}{16} a^2 x^4 y(x)+\frac {a^3 x^6}{64}+\frac {a^2 x^4}{16}+\frac {3}{16} a b^2 x^4+\frac {3}{4} a b x^3 y(x)+\frac {1}{4} a b x^3+\frac {3}{4} a x^2 y(x)^2+\frac {1}{2} a x^2 y(x)-\frac {a x}{2}+\frac {3}{4} b^2 x^2 y(x)+\frac {b^3 x^3}{8}+\frac {b^2 x^2}{4}+\frac {3}{2} b x y(x)^2+b x y(x)+y(x)^3+y(x)^2+1 \] Mathematica : cpu = 0.489696 (sec), leaf count = 141

\[\text {Solve}\left [-\frac {1}{3} (27 b+58)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (27 b+58)^{2/3}-3\ 2^{2/3} \text {$\#$1}+(27 b+58)^{2/3}\& ,\frac {\log \left (\frac {\sqrt [3]{2} \left (\frac {1}{4} \left (3 a x^2+6 b x+4\right )+3 y(x)\right )}{\sqrt [3]{27 b+58}}-\text {$\#$1}\right )}{2^{2/3}-\text {$\#$1}^2 (27 b+58)^{2/3}}\& \right ]=\frac {(27 b+58)^{2/3} x}{9\ 2^{2/3}}+c_1,y(x)\right ]\] Maple : cpu = 0.227 (sec), leaf count = 42

\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}-{\frac {bx}{2}}+{\it RootOf} \left ( -x+2\,\int ^{{\it \_Z}}\! \left ( 2\,{{\it \_a}}^{3}+2\,{{\it \_a}}^{2}+b+2 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]