Internal problem ID [5329]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page
65
Problem number: 23.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{2}-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y = \frac {x^{2}}{4} y = -c_{1}^{2}+c_{1} x \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[y'[x]^2-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-c_1) y(x)\to \frac {x^2}{4} \end{align*}