Internal problem ID [4282]
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]
\[ \boxed {2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}=x} \]
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 69
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 \left (x \right ) = \left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) x y \left (x \right ) = \left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) x y \left (x \right ) = -x y \left (x \right ) = -\frac {\left (-\frac {2 \left (c_{1} x \right )^{\frac {3}{2}}}{c_{1}^{3}}+1\right ) c_{1}}{3} y \left (x \right ) = -\frac {\left (\frac {2 \left (c_{1} x \right )^{\frac {3}{2}}}{c_{1}^{3}}+1\right ) c_{1}}{3} \end{align*}
✓ Solution by Mathematica
Time used: 28.499 (sec). Leaf size: 4317
DSolve[2 x (y'[x])^3 - 3 y[x] (y'[x])^2 -x==0,y[x],x,IncludeSingularSolutions -> True]
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