Internal problem ID [2490]
Book: Applied Differential equations, N Curle, 1971
Section: Examples, page 35
Problem number: 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
Solve \begin {gather*} \boxed {\left (y-y^{\prime } x \right )^{2}-1-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 46
dsolve((y(x)-x*diff(y(x),x))^2=1+(diff(y(x),x))^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = x c_{1}-\sqrt {c_{1}^{2}+1} \\ y \relax (x ) = x c_{1}+\sqrt {c_{1}^{2}+1} \\ y \relax (x ) = c_{1} \sqrt {x -1}\, \sqrt {x +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 73
DSolve[(y[x]-x*y'[x])^2==1+(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\sqrt {1+c_1{}^2} \\ y(x)\to c_1 x+\sqrt {1+c_1{}^2} \\ y(x)\to -\sqrt {1-x^2} \\ y(x)\to \sqrt {1-x^2} \\ \end{align*}