2.532   ODE No. 532

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

\[ a y'(x)^3+b y'(x)^2+c y'(x)-d-y(x)=0 \] Mathematica : cpu = 3599.94 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.15 (sec), leaf count = 1211

\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {a\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}}{ \left ( 108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3} \right ) ^{2/3}-2\,b\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}-12\,ca+4\,{b}^{2}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {a\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}}{ \left ( i\sqrt {3}-1 \right ) \left ( i\sqrt {3}\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}b-6\,i\sqrt {3}ac+2\,i\sqrt {3}{b}^{2}+ \left ( 108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3} \right ) ^{2/3}+b\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}+6\,ca-2\,{b}^{2} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {a\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}}{ \left ( i\sqrt {3}+1 \right ) \left ( i\sqrt {3}\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}b-6\,i\sqrt {3}ac+2\,i\sqrt {3}{b}^{2}- \left ( 108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3} \right ) ^{2/3}-b\sqrt [3]{108\,{a}^{2}{\it \_a}+12\,\sqrt {3}\sqrt {27\,{a}^{2}{{\it \_a}}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,bca-8\,{b}^{3}}-6\,ca+2\,{b}^{2} \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \]