73.15.31 problem 22.10 (d)

Internal problem ID [15391]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.10 (d)
Date solved : Monday, March 31, 2025 at 01:36:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = 6*exp(-5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{5 x}+\frac {3 \,{\mathrm e}^{-5 x}}{50} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 28

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==6*Exp[-5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 e^{-5 x}}{50}+e^{5 x} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.233 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 6*exp(-5*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{5 x} + \frac {3 e^{- 5 x}}{50} \]