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 = 300.009 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.37 (sec), leaf count = 944

\[ \left \{ x-\int ^{y \left ( x \right ) }\!-3\,{\sqrt [3]{6}a\sqrt [3]{27}\sqrt [3]{\sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) } \left ( 3\,{6}^{2/3}ac-{6}^{2/3}{b}^{2}+\sqrt [3]{6}b\sqrt [3]{27}\sqrt [3]{\sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) }-{27}^{2/3} \left ( \sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) \right ) ^{2/3} \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {\sqrt [3]{3}\sqrt [3]{2}a\sqrt [3]{27}}{1+i\sqrt {3}}\sqrt [3]{\sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) } \left ( -2\,{27}^{2/3} \left ( \sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) \right ) ^{2/3}+ \left ( i{3}^{5/6}-\sqrt [3]{3} \right ) \sqrt [3]{2}b\sqrt [3]{27}\sqrt [3]{\sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) }-9\,{2}^{2/3} \left ( i\sqrt [6]{3}+1/3\,{3}^{2/3} \right ) \left ( ac-1/3\,{b}^{2} \right ) \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {\sqrt [3]{3}\sqrt [3]{2}a\sqrt [3]{27}}{i\sqrt {3}-1}\sqrt [3]{\sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) } \left ( 2\,{27}^{2/3} \left ( \sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) \right ) ^{2/3}+\sqrt [3]{2} \left ( i{3}^{5/6}+\sqrt [3]{3} \right ) b\sqrt [3]{27}\sqrt [3]{\sqrt {3} \left ( 1/3\,\sqrt {27\, \left ( d+{\it \_a} \right ) ^{2}{a}^{2}+18\,c \left ( \left ( d+{\it \_a} \right ) b+2/9\,{c}^{2} \right ) a+ \left ( -4\,d-4\,{\it \_a} \right ) {b}^{3}-{b}^{2}{c}^{2}}a+ \left ( \left ( d+{\it \_a} \right ) {a}^{2}+1/3\,abc-{\frac {2\,{b}^{3}}{27}} \right ) \sqrt {3} \right ) }-9\,{2}^{2/3} \left ( i\sqrt [6]{3}-1/3\,{3}^{2/3} \right ) \left ( ac-1/3\,{b}^{2} \right ) \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0 \right \} \]