Internal problem ID [4275]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1054.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 393
dsolve(2*diff(y(x),x)^3+diff(y(x),x)^2-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ 6 \sqrt {3}\, \left (\int _{}^{y \left (x \right )}\frac {\left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}}{-3^{\frac {1}{3}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {2}{3}}+\sqrt {3}\, \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}-3^{\frac {2}{3}}}d \textit {\_a} \right )+x -c_{1} &= 0 \\ \frac {24 i \sqrt {3}\, \left (\int _{}^{y \left (x \right )}\frac {\left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}}{\left (3^{\frac {1}{3}}+3^{\frac {1}{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}\right ) \left (i 3^{\frac {5}{6}}+3^{\frac {1}{3}}-2 \,3^{\frac {1}{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}\right )}d \textit {\_a} \right )+\left (x -c_{1} \right ) \left (-i+\sqrt {3}\right )}{-i+\sqrt {3}} &= 0 \\ \frac {24 i \sqrt {3}\, \left (\int _{}^{y \left (x \right )}\frac {\left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}}{\left (i 3^{\frac {5}{6}}-3^{\frac {1}{3}}+2 \,3^{\frac {1}{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}\right ) \left (3^{\frac {1}{3}}+3^{\frac {1}{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{\frac {1}{3}}\right )}d \textit {\_a} \right )+\left (x -c_{1} \right ) \left (\sqrt {3}+i\right )}{\sqrt {3}+i} &= 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2 (y'[x])^3 + (y'[x])^2 - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out