Internal problem ID [2999]
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]
\[ \boxed {\left (-x y^{\prime }+y\right )^{2}-{y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 57
dsolve((y(x)-x*diff(y(x),x))^2=1+(diff(y(x),x))^2,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: 0.127 (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*}