Internal problem ID [4458]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-{\mathrm e}^{x} x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = {\mathrm e}-1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(y(x),x)-y(x)/x=x*exp(x),y(1) = exp(1)-1],y(x), singsol=all)
\[ y \relax (x ) = \left ({\mathrm e}^{x}-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 12
DSolve[{y'[x]-y[x]/x==x*Exp[x],{y[1]==Exp[1]-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (e^x-1\right ) x \\ \end{align*}