Internal problem ID [4322]
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], _rational, _Clairaut]
\[ \boxed {\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.343 (sec). Leaf size: 21
dsolve(sqrt(a^2+b^2*diff(y(x),x)^2)+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {b^{2} c_{1}^{2}+a^{2}}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.383 (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*}