44.6.23 problem 23

Internal problem ID [7167]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 23
Date solved : Tuesday, February 04, 2025 at 12:43:22 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\left (3 x +1\right ) y&={\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(x*diff(y(x),x)+(3*x+1)*y(x)=exp(-3*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-3 x} \left (x +c_1 \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 18

DSolve[x*D[y[x],x]+(3*x+1)*y[x]==Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-3 x} (x+c_1)}{x} \]