75.5.10 problem 10

Internal problem ID [19958]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 10
Date solved : Thursday, October 02, 2025 at 05:04:28 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\[ y = -\frac {x}{4}+\frac {1}{4}+c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 38

ode=D[y[x],{x,3}]+D[y[x],{x,2}]-4D[y[x],x]-4*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x}{4}+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^{2 x}+\frac {1}{4} \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 4*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{- x} + C_{3} e^{2 x} - \frac {x}{4} + \frac {1}{4} \]