15.21.2 problem 24

Internal problem ID [3326]
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
Date solved : Monday, January 27, 2025 at 07:34:14 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: 0.033 (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: 0.015 (sec). Leaf size: 41

DSolve[y[x]==D[y[x],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*}