Internal problem ID [4033]
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]
\[ \boxed {{y^{\prime }}^{2}-2 x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 20
dsolve(diff(y(x),x)^2-2*x*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2} \\ y \left (x \right ) &= -\frac {c_{1} \left (-2 x +c_{1} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (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*}