7.4.3 problem 3

Internal problem ID [75]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 3
Date solved : Friday, February 07, 2025 at 07:48:22 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(y(x),x)+ 3*y(x)=2*x*exp(-3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-3 x} \left (x^{2}+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 17

DSolve[D[y[x],x]+ 3*y[x]==2*x*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (x^2+c_1\right ) \]