83.5.8 problem 8

Internal problem ID [19103]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:56:14 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 18

dsolve(y(x)^2+(x-1/y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {1}{-\operatorname {LambertW}\left (c_{1} {\mathrm e}^{x -1}\right )-1+x} \]

✓ Solution by Mathematica

Time used: 60.080 (sec). Leaf size: 21

DSolve[y[x]^2+(x-1/y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{-W\left (c_1 e^{x-1}\right )+x-1} \]