62.18.1 problem Ex 1

Internal problem ID [12912]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 30. Page 63
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:43:19 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: 0.066 (sec). Leaf size: 27

dsolve(y(x)=diff(y(x),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: 0.016 (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*}