18.1.18 problem Problem 14.24 (a)

Internal problem ID [3474]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.24 (a)
Date solved : Monday, January 27, 2025 at 07:38:20 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{x}&=1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 10

dsolve([diff(y(x),x)-y(x)/x=1,y(1) = -1],y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (-1+\ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 11

DSolve[{D[y[x],x]-y[x]/x==1,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (\log (x)-1) \]