82.25.1 problem Ex. 1

Internal problem ID [18792]
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 66
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 12:59:06 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 27

ode=D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (e^{3 x} (c_3 x+c_2)+c_1\right ) \]

✓ Sympy. Time used: 0.089 (sec). Leaf size: 17

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

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