23.5.36 problem 36

Internal problem ID [6645]
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 : 36
Date solved : Tuesday, September 30, 2025 at 03:50:29 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

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

ode:=-3*diff(y(x),x)-2*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 28

ode=-3*D[y[x],x] - 2*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}{3} c_2 e^{3 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 15

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

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