44.10.3 problem 1(c)

Internal problem ID [9258]
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 : Tuesday, September 30, 2025 at 06:15:45 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*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+10*diff(y(x),x)+25*y(x) = 14*exp(-5*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to e^{-5 x} \left (7 x^2+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) + 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 14*exp(-5*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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