50.10.3 problem 1(c)

Internal problem ID [7972]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:34:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+10*diff(y(x),x)+25*y(x)=14*exp(-5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-5 x} \left (c_{1} x +7 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+10*D[y[x],x]+25*y[x]==14*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (7 x^2+c_2 x+c_1\right ) \]