73.15.24 problem 22.9 (b)

Internal problem ID [15384]
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 : 22.9 (b)
Date solved : Monday, March 31, 2025 at 01:36:09 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 22

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

\[ y(x)\to 5 x-\frac {1}{4} c_1 e^{-4 x}+c_2 \]

✓ Sympy. Time used: 0.165 (sec). Leaf size: 14

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

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