Internal problem ID [6308]
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]
Solve \begin {gather*} \boxed {\frac {\left (y^{\prime }\right )^{2}}{4}-x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (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 \relax (x ) = x^{2} \\ y \relax (x ) = -\frac {1}{4} c_{1}^{2}+c_{1} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (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*}