Internal problem ID [5504]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }-y-2 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 9
dsolve([x*diff(y(x),x)-y(x)=2*x,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = 2 \ln \relax (x ) x \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 10
DSolve[{x*y'[x]-y[x]==2*x,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \log (x) \\ \end{align*}