Internal problem ID [2361]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 39, page 179
Problem number: 30.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {\left (y-y^{\prime } x \right )^{2}-{y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 46
dsolve((y(x)-diff(y(x),x)*x)^2=diff(y(x),x)^2+1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} x -\sqrt {c_{1}^{2}+1} y \left (x \right ) = c_{1} x +\sqrt {c_{1}^{2}+1} y \left (x \right ) = \sqrt {x -1}\, \sqrt {x +1}\, c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 73
DSolve[(y[x]-y'[x]*x)^2==y'[x]^2+1,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*}