23.5.43 problem 43

Internal problem ID [6652]
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 : 43
Date solved : Tuesday, September 30, 2025 at 03:50:32 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

ode=-3*y[x] - D[y[x],x] + 3*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 c_1 e^{-3 x}+c_2 e^{-x}+c_3 e^x \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 19

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

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