8.4.3 problem 3

Internal problem ID [706]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:58:38 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 17

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

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