36.2.17 problem 17

Internal problem ID [6310]
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
Date solved : Monday, January 27, 2025 at 01:55:47 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (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: 0.050 (sec). Leaf size: 12

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

\[ y(x)\to \left (e^x-1\right ) x \]