Internal problem ID [4966]
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]
\[ \boxed {y^{\prime }-\frac {y}{x}={\mathrm e}^{x} x} \] With initial conditions \begin {align*} [y \left (1\right ) = {\mathrm e}-1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve([diff(y(x),x)-y(x)/x=x*exp(x),y(1) = -1+exp(1)],y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{x}-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 12
DSolve[{y'[x]-y[x]/x==x*Exp[x],{y[1]==Exp[1]-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (e^x-1\right ) x \]