69.1.69 problem 97

Internal problem ID [14222]
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
Date solved : Tuesday, January 28, 2025 at 06:22:31 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

\begin{align*} y&=x y^{\prime }+\frac {1}{y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 27

dsolve(y(x)=x*diff(y(x),x)+1/diff(y(x),x),y(x), singsol=all)
 

\begin{align*} y &= -2 \sqrt {x} \\ y &= 2 \sqrt {x} \\ y &= c_{1} x +\frac {1}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 41

DSolve[y[x]==x*D[y[x],x]+1/D[y[x],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*}