82.28.1 problem Ex. 1

Internal problem ID [18809]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 75
Problem number : Ex. 1
Date solved : Monday, March 31, 2025 at 06:15:28 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y&=3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 52

ode:=diff(diff(diff(y(x),x),x),x)+y(x) = 3+exp(-x)+5*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\frac {{\mathrm e}^{-x} \left (9 c_1 +3 x +3\right )}{9}+\frac {5 \,{\mathrm e}^{2 x}}{9}+3 \]

✓ Mathematica. Time used: 1.836 (sec). Leaf size: 79

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

\[ y(x)\to \frac {1}{9} e^{-x} \left (3 x+27 e^x+5 e^{3 x}+9 c_3 e^{3 x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+9 c_2 e^{3 x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+3+9 c_1\right ) \]

✓ Sympy. Time used: 0.176 (sec). Leaf size: 49

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

\[ y{\left (x \right )} = \left (C_{1} + \frac {x}{3}\right ) e^{- x} + \left (C_{2} \sin {\left (\frac {\sqrt {3} x}{2} \right )} + C_{3} \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{\frac {x}{2}} + \frac {5 e^{2 x}}{9} + 3 \]