Internal problem ID [2355]
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: 24.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Clairaut]
\[ \boxed {y-x y^{\prime }-\frac {1}{y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 27
dsolve(y(x)=diff(y(x),x)*x+1/diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \sqrt {x} \\ y \left (x \right ) &= 2 \sqrt {x} \\ y \left (x \right ) &= c_{1} x +\frac {1}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 41
DSolve[y[x]==y'[x]*x+1/y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\frac {1}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {x} \\ y(x)\to 2 \sqrt {x} \\ \end{align*}