Internal problem ID [3910]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 13.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
Solve \begin {gather*} \boxed {y-y^{\prime } x -\sqrt {b^{2}-\left (y^{\prime }\right )^{2} a^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 36
dsolve(y(x)=x*diff(y(x),x)+sqrt(b^2-a^2*(diff(y(x),x))^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x +\sqrt {-a^{2} c_{1}^{2}+b^{2}} \\ y \relax (x ) = \sqrt {a^{2}+x^{2}}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.367 (sec). Leaf size: 38
DSolve[y[x]==x*y'[x]+Sqrt[b^2-a^2*(y'[x])^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {b^2-a^2 c_1{}^2}+c_1 x \\ y(x)\to \sqrt {b^2} \\ \end{align*}