82.33.7 problem Ex. 7

Internal problem ID [18821]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 7
Date solved : Thursday, March 13, 2025 at 01:00:04 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y&=x \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 36

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)-6*diff(y(x),x)+8*y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (\left (x +\frac {3}{4}\right ) {\mathrm e}^{2 x}+8 \,{\mathrm e}^{3 x} c_{1} +8 c_3 \,{\mathrm e}^{6 x}+8 c_{2} \right ) {\mathrm e}^{-2 x}}{8} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 36

ode=D[y[x],{x,3}]-3*D[y[x],{x,2}]-6*D[y[x],x]+8*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x}{8}+c_1 e^{-2 x}+c_2 e^x+c_3 e^{4 x}+\frac {3}{32} \]

✓ Sympy. Time used: 0.201 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + 8*y(x) - 6*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{x} + C_{3} e^{4 x} + \frac {x}{8} + \frac {3}{32} \]