Internal problem ID [6036]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES
Page 314
Problem number: 11.
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}-x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.313 (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 \relax (x ) = \frac {x^{2}}{4} \\ y \relax (x ) = c_{1} x -c_{1}^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (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*}