Internal problem ID [2317]
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: 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x \left (-1+{y^{\prime }}^{2}\right )-2 y y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 32
dsolve(x*(diff(y(x),x)^2-1)=2*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -i x \\ y \left (x \right ) &= i x \\ y \left (x \right ) &= \frac {-c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 71
DSolve[x*(y'[x]^2-1)==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*}