23.5.26 problem 26

Internal problem ID [6635]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 03:50:25 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to e^{-x} \left (c_3 e^{2 x}+c_2 \cos \left (\sqrt {2} x\right )+c_1 \sin \left (\sqrt {2} x\right )\right ) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 31

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

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