Internal problem ID [3774]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1062.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {2 x \left (y^{\prime }\right )^{3}-3 y \left (y^{\prime }\right )^{2}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.457 (sec). Leaf size: 88
dsolve(2*x*diff(y(x),x)^3-3*y(x)*diff(y(x),x)^2-x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = -\frac {\left (-\frac {2 \left (c_{1} x \right )^{\frac {3}{2}}}{c_{1}^{3}}+1\right ) c_{1}}{3} \\ y \relax (x ) = -\frac {\left (\frac {2 \left (c_{1} x \right )^{\frac {3}{2}}}{c_{1}^{3}}+1\right ) c_{1}}{3} \\ y \relax (x ) = \frac {x}{2}-\frac {\sqrt {3}\, x \tan \left (\RootOf \left (\sqrt {3}\, \ln \left (\frac {3 x^{2}}{4}+\frac {3 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{2}}{4}\right )+2 \sqrt {3}\, c_{1}+2 \textit {\_Z} \right )\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 146.523 (sec). Leaf size: 14841
DSolve[2 x (y'[x])^3 - 3 y[x] (y'[x])^2 -x==0,y[x],x,IncludeSingularSolutions -> True]
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