Internal problem ID [11232]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first.
Article 28. Summary. Page 59
Problem number: Ex 8.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}=1} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 57
dsolve((1+x^2)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+y(x)^2-1=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {x^{2}+1} \\ y \left (x \right ) &= -\sqrt {x^{2}+1} \\ y \left (x \right ) &= c_{1} x -\sqrt {-c_{1}^{2}+1} \\ y \left (x \right ) &= c_{1} x +\sqrt {-c_{1}^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 73
DSolve[(1+x^2)*(y'[x])^2-2*x*y[x]*y'[x]+y[x]^2-1==0,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 {x^2+1} \\ y(x)\to \sqrt {x^2+1} \\ \end{align*}