Internal problem ID [2329]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 16.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x \left (-1+{y^{\prime }}^{2}\right )-2 y^{\prime } y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((diff(y(x),x)^2-1)*x=2*diff(y(x),x)*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\left (-\frac {x^{2}}{c_{1}^{2}}+1\right ) c_{1}}{2} y \left (x \right ) = c_{1} x \end{align*}
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 71
DSolve[(y'[x]^2-1)*x==2*y'[x]*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-c_1} \left (-x^2+e^{2 c_1}\right ) y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right ) y(x)\to -i x y(x)\to i x \end{align*}