Internal problem ID [11690]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (\frac {1}{y}-a \right ) y^{\prime }=-\frac {2}{x}+b} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((1/y(x)-a)*diff(y(x),x)+2/x-b=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-\frac {a \,{\mathrm e}^{b x} c_{1}}{x^{2}}\right )}{a} \]
✓ Solution by Mathematica
Time used: 6.296 (sec). Leaf size: 32
DSolve[(1/y[x]-a)*y'[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*}