Internal problem ID [3814]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1123.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\sqrt {a^{2}+b^{2} \left (y^{\prime }\right )^{2}}+y^{\prime } x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 37
dsolve(sqrt(a^2+b^2*diff(y(x),x)^2)+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {b^{2} c_{1}^{2}+a^{2}}+c_{1} x \\ y \relax (x ) = c_{1} \sqrt {-b^{2}+x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.412 (sec). Leaf size: 37
DSolve[Sqrt[a^2+b^2 (y'[x])^2] +x y'[x] -y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {a^2+b^2 c_1{}^2}+c_1 x \\ y(x)\to \sqrt {a^2} \\ \end{align*}