Internal problem ID [3767]
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]
Solve \begin {gather*} \boxed {2 \left (y^{\prime }\right )^{3}+\left (y^{\prime }\right )^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 372
dsolve(2*diff(y(x),x)^3+diff(y(x),x)^2-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {6 \,3^{\frac {1}{3}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {1}{3}}}{3^{\frac {1}{3}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {2}{3}}+3^{\frac {1}{3}}-\left (\sqrt {3}\, \left (54 \sqrt {3}\, \textit {\_a} -\sqrt {3}+18 \sqrt {\textit {\_a} \left (-1+27 \textit {\_a} \right )}\right )\right )^{\frac {1}{3}}}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}-\frac {12 \,3^{\frac {1}{3}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {1}{3}}}{i 3^{\frac {5}{6}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {2}{3}}-i 3^{\frac {5}{6}}+3^{\frac {1}{3}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {2}{3}}+3^{\frac {1}{3}}+2 \left (\sqrt {3}\, \left (54 \sqrt {3}\, \textit {\_a} -\sqrt {3}+18 \sqrt {\textit {\_a} \left (-1+27 \textit {\_a} \right )}\right )\right )^{\frac {1}{3}}}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {12 \,3^{\frac {1}{3}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {1}{3}}}{i 3^{\frac {5}{6}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {2}{3}}-i 3^{\frac {5}{6}}-3^{\frac {1}{3}} \left (-1+54 \textit {\_a} +6 \sqrt {81 \textit {\_a}^{2}-3 \textit {\_a}}\right )^{\frac {2}{3}}-3^{\frac {1}{3}}-2 \left (\sqrt {3}\, \left (54 \sqrt {3}\, \textit {\_a} -\sqrt {3}+18 \sqrt {\textit {\_a} \left (-1+27 \textit {\_a} \right )}\right )\right )^{\frac {1}{3}}}d \textit {\_a} \right )-c_{1} = 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