Internal problem ID [3525]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 793.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 y^{\prime } x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2-2*x*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{2} \\ y \relax (x ) = -\frac {1}{2} c_{1}^{2}+c_{1} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 29
DSolve[(y'[x])^2-2 x y'[x]+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {c_1{}^2}{2} \\ y(x)\to \frac {x^2}{2} \\ \end{align*}