44.6.19 problem 19

Internal problem ID [7163]
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 : 19
Date solved : Tuesday, February 04, 2025 at 12:42:53 AM
CAS classification : [_linear]

\begin{align*} \left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=2 \,{\mathrm e}^{-x} x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve((x+1)*diff(y(x),x)+(x+2)*y(x)=2*x*exp(-x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-x} \left (x^{2}+c_1 \right )}{x +1} \]

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 22

DSolve[(x+1)*D[y[x],x]+(x+2)*y[x]==2*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x} \left (x^2+c_1\right )}{x+1} \]