73.15.3 problem 22.1 (c)

Internal problem ID [15363]
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 : 22.1 (c)
Date solved : Monday, March 31, 2025 at 01:35:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=30 \,{\mathrm e}^{-4 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)-5*y(x) = 30*exp(-4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{6 x}-6 \,{\mathrm e}^{x}+c_1 \right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 27

ode=D[y[x],{x,2}]+4*D[y[x],x]-5*y[x]==30*Exp[-4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-5 x} \left (-6 e^x+c_2 e^{6 x}+c_1\right ) \]

✓ Sympy. Time used: 0.243 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 30*exp(-4*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{x} - 6 e^{- 4 x} \]