23.5.27 problem 27

Internal problem ID [6636]
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 : 27
Date solved : Tuesday, September 30, 2025 at 03:50:25 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} -2 y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=-2*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);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 28

ode=-2*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 c_1 \left (-e^{-x}\right )+\frac {1}{2} c_2 e^{2 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 15

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

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