Internal problem ID [2362]
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: 31.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Clairaut]
\[ \boxed {{y^{\prime }}^{2} x -y^{\prime } y=2} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2*x-diff(y(x),x)*y(x)-2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} x -\frac {2}{c_{1}} y \left (x \right ) = c_{1} \sqrt {x} \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 57
DSolve[y'[x]^2*x-y'[x]*y[x]-2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {2}{c_1} y(x)\to \text {Indeterminate} y(x)\to -2 i \sqrt {2} \sqrt {x} y(x)\to 2 i \sqrt {2} \sqrt {x} \end{align*}