Internal problem ID [3531]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 799.
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}-a x y^{\prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.089 (sec). Leaf size: 25
dsolve(diff(y(x),x)^2-a*x*diff(y(x),x)+a*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {a \,x^{2}}{4} \\ y \relax (x ) = c_{1} x -\frac {c_{1}^{2}}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[(y'[x])^2-a x y'[x]+a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x-\frac {c_1}{a}\right ) \\ y(x)\to \frac {a x^2}{4} \\ \end{align*}