64.5.15 problem 15

Internal problem ID [13328]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 05:22:26 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

dsolve(diff(y(x),x)-y(x)/x=-y(x)^2/x,y(x), singsol=all)
 

\[ y = \frac {x}{x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.262 (sec). Leaf size: 43

DSolve[D[y[x],x]-y[x]/x==-y[x]^2/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ][-\log (x)+c_1] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}