Internal problem ID [6307]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 17.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {\frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 19
dsolve((1/4)*diff(y(x),x)^2-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = x^{2} \\ y \left (x \right ) = -\frac {1}{4} c_{1}^{2}+c_{1} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 25
DSolve[(1/4)*(y'[x])^2-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {c_1{}^2}{4} \\ y(x)\to x^2 \\ \end{align*}