3.944   ODE No. 944

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-32\,axy \left ( x \right ) -8\,{a}^{2}{x}^{3}-16\,a{x}^{2}b-32\,ax+64\, \left ( y \left ( x \right ) \right ) ^{3}+48\,a{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+96\, \left ( y \left ( x \right ) \right ) ^{2}bx+12\,y \left ( x \right ) {a}^{2}{x}^{4}+48\,y \left ( x \right ) a{x}^{3}b+48\,y \left ( x \right ) {b}^{2}{x}^{2}+{a}^{3}{x}^{6}+6\,{a}^{2}{x}^{5}b+12\,a{x}^{4}{b}^{2}+8\,{b}^{3}{x}^{3}}{64\,y \left ( x \right ) +16\,a{x}^{2}+32\,bx+64}}=0} \]

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

Mathematica: cpu = 1.613205 (sec), leaf count = 233 \[ \text {Solve}\left [x-4 \text {RootSum}\left [\text {$\#$1}^6 a^3+6 \text {$\#$1}^5 a^2 b+12 \text {$\#$1}^4 a^2 y(x)+12 \text {$\#$1}^4 a b^2+48 \text {$\#$1}^3 a b y(x)+8 \text {$\#$1}^3 b^3+8 \text {$\#$1}^2 a b+48 \text {$\#$1}^2 a y(x)^2+48 \text {$\#$1}^2 b^2 y(x)+16 \text {$\#$1} b^2+96 \text {$\#$1} b y(x)^2+32 b y(x)+32 b+64 y(x)^3\& ,\frac {\text {$\#$1}^2 a \log (x-\text {$\#$1})+2 \text {$\#$1} b \log (x-\text {$\#$1})+4 y(x) \log (x-\text {$\#$1})+4 \log (x-\text {$\#$1})}{3 \text {$\#$1}^4 a^2+12 \text {$\#$1}^3 a b+24 \text {$\#$1}^2 a y(x)+12 \text {$\#$1}^2 b^2+48 \text {$\#$1} b y(x)+8 b+48 y(x)^2}\& \right ]=c_1,y(x)\right ] \]

Maple: cpu = 0.062 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}-{\frac {bx}{2}}+{ \it RootOf} \left ( bx+2\,\int ^{{\it \_Z}}\!-{\frac {b \left ( {\it \_a }+1 \right ) }{2\,{{\it \_a}}^{3}+{\it \_a}\,b+b}}{d{\it \_a}}+2\,{\it \_C1} \right ) \right \} \]