15.2.1 problem 1

Internal problem ID [2871]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:21:17 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 10

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

\[ y = \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 12

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

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