Internal problem ID [4022]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 782.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{2}-x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 19
dsolve(diff(y(x),x)^2-x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}}{4} \\ y \left (x \right ) &= c_{1} \left (-c_{1} +x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (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*}