64.4.8 problem 8

Internal problem ID [13297]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:16:25 AM
CAS classification : [_linear]

\begin{align*} x +y-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 10

dsolve((x+y(x))- x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = x \left (\ln \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 12

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

\[ y(x)\to x (\log (x)+c_1) \]