50.14.17 problem 3(a)

Internal problem ID [8055]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 3(a)
Date solved : Monday, January 27, 2025 at 03:40:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=2 x -1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=2*x-1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==2*x-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+c_1 e^{-2 x}+c_2 e^{-x}-2 \]