12.5.18 problem 15

Internal problem ID [1642]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 15
Date solved : Monday, January 27, 2025 at 05:15:38 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 12

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

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