Internal problem ID [1994]
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) .
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 10
dsolve([diff(y(x),x)-y(x)/x=1,y(1) = -1],y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \relax (x )-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 11
DSolve[{y'[x]-y[x]/x==1,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (\log (x)-1) \\ \end{align*}