76.33.28 problem Ex. 28

Internal problem ID [20206]
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. 28
Date solved : Thursday, October 02, 2025 at 05:34:40 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+4*y(x) = exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 x +c_2 \right ) {\mathrm e}^{2 x}+c_1 \,{\mathrm e}^{-x}+\frac {{\mathrm e}^{3 x}}{4} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to \frac {e^{3 x}}{4}+c_1 e^{-x}+e^{2 x} (c_3 x+c_2) \end{align*}

✓ Sympy. Time used: 0.065 (sec). Leaf size: 24

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

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