Internal problem ID [12166]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 97.
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: 0.032 (sec). Leaf size: 27
dsolve(y(x)=x*diff(y(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: 0.017 (sec). Leaf size: 41
DSolve[y[x]==x*y'[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*}