Internal problem ID [3815]
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], _Clairaut]
Solve \begin {gather*} \boxed {a \sqrt {1+\left (y^{\prime }\right )^{2}}+x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.186 (sec). Leaf size: 33
dsolve(a*sqrt(1+diff(y(x),x)^2)+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = a \sqrt {c_{1}^{2}+1}+c_{1} x \\ y \relax (x ) = c_{1} \sqrt {-a^{2}+x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.051 (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*}