2.524   ODE No. 524

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

\[ y'(x)^3-2 y(x) y'(x)+y(x)^2=0 \] Mathematica : cpu = 0.020245 (sec), leaf count = 422

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2}}{\sqrt [3]{2} \left (\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2\right )^{2/3}+4 \sqrt [3]{3} \text {$\#$1}}d\text {$\#$1}\& \right ]\left [\frac {x}{6^{2/3}}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2}}{\sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2\right )^{2/3}-\sqrt [3]{2} \sqrt [6]{3} i \left (\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2\right )^{2/3}-12 \text {$\#$1}-4 i \text {$\#$1} \sqrt {3}}d\text {$\#$1}\& \right ]\left [c_1-\frac {i x}{2\ 2^{2/3} 3^{5/6}}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2}}{\sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2\right )^{2/3}+\sqrt [3]{2} \sqrt [6]{3} i \left (\sqrt {3} \sqrt {\text {$\#$1}^3 (27 \text {$\#$1}-32)}-9 \text {$\#$1}^2\right )^{2/3}-12 \text {$\#$1}+4 i \text {$\#$1} \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {i x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \}\right \}\] Maple : cpu = 0.207 (sec), leaf count = 243

\[\left \{-c_{1}+x -\left (\int _{}^{y \left (x \right )}\frac {12 \left (-108 \textit {\_a}^{2}+12 \sqrt {81 \textit {\_a}^{4}-96 \textit {\_a}^{3}}\right )^{\frac {1}{3}}}{12 \left (i \sqrt {3}-1\right )^{2} \textit {\_a} +\left (i \sqrt {3}-1\right ) \left (-108 \textit {\_a}^{2}+12 \sqrt {81 \textit {\_a}^{4}-96 \textit {\_a}^{3}}\right )^{\frac {2}{3}}}d \textit {\_a} \right ) = 0, -c_{1}+x -\left (\int _{}^{y \left (x \right )}\frac {6 \left (-108 \textit {\_a}^{2}+12 \sqrt {81 \textit {\_a}^{4}-96 \textit {\_a}^{3}}\right )^{\frac {1}{3}}}{24 \textit {\_a} +\left (-108 \textit {\_a}^{2}+12 \sqrt {81 \textit {\_a}^{4}-96 \textit {\_a}^{3}}\right )^{\frac {2}{3}}}d \textit {\_a} \right ) = 0, -c_{1}+x -\left (\int _{}^{y \left (x \right )}\frac {12 \left (-108 \textit {\_a}^{2}+12 \sqrt {81 \textit {\_a}^{4}-96 \textit {\_a}^{3}}\right )^{\frac {1}{3}}}{\left (1+i \sqrt {3}\right ) \left (12 i \sqrt {3}\, \textit {\_a} +12 \textit {\_a} -\left (-108 \textit {\_a}^{2}+12 \sqrt {81 \textit {\_a}^{4}-96 \textit {\_a}^{3}}\right )^{\frac {2}{3}}\right )}d \textit {\_a} \right ) = 0\right \}\]