65.5.7 problem 10.3 (ii)

Internal problem ID [13746]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.3 (ii)
Date solved : Tuesday, January 28, 2025 at 06:01:07 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 21

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

\[ y = -\frac {\operatorname {LambertW}\left (-\frac {a \,{\mathrm e}^{b x} c_{1}}{x^{2}}\right )}{a} \]

✓ Solution by Mathematica

Time used: 3.029 (sec). Leaf size: 32

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

\begin{align*} y(x)\to -\frac {W\left (-\frac {a e^{b x-c_1}}{x^2}\right )}{a} \\ y(x)\to 0 \\ \end{align*}