81.5.5 problem 5

Internal problem ID [18589]
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 : 5
Date solved : Thursday, March 13, 2025 at 12:24:31 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

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

\[ y \left (x \right ) = \frac {x^{2}}{12}-\frac {c_{2} {\mathrm e}^{-3 x}}{3}-\frac {{\mathrm e}^{-2 x} c_{1}}{2}-\frac {5 x}{36}+c_3 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 42

ode=D[y[x],{x,3}]+5*D[y[x],{x,2}]+6*D[y[x],x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^2}{12}-\frac {5 x}{36}-\frac {1}{3} c_1 e^{-3 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]

✓ Sympy. Time used: 0.213 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + 6*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 3 x} + C_{3} e^{- 2 x} + \frac {x^{2}}{12} - \frac {5 x}{36} \]