89.15.4 problem 4

Internal problem ID [24638]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Oral Exercises at page 131
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:46:39 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=20 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)-5*y(x) = 20; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{-5 x} c_1 -4 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 21

ode=D[y[x],{x,2}]+4*D[y[x],{x,1}]-5*y[x]==20; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-5 x}+c_2 e^x-4 \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 20,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{x} - 4 \]