Internal problem ID [4323]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1125.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 17
dsolve(a*sqrt(1+diff(y(x),x)^2)+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = a \sqrt {c_{1}^{2}+1}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 27
DSolve[a Sqrt[1+(y'[x])^2] + x y'[x] -y[x]==0 y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a \sqrt {1+c_1{}^2}+c_1 x y(x)\to a \end{align*}