5.18 problem 15

Internal problem ID [992]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +y}{x}=0} \end {gather*}

Solution by Maple

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

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

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

Solution by Mathematica

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

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

\begin{align*} y(x)\to x (\log (x)+c_1) \\ \end{align*}