50.3.4 problem 1(d)

Internal problem ID [7828]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:24:22 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 29

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

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