23.5.52 problem 52

Internal problem ID [6661]
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 : 52
Date solved : Tuesday, September 30, 2025 at 03:50:36 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} -2 y+5 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=-2*y(x)+5*diff(y(x),x)-4*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 22

ode=-2*y[x] + 5*D[y[x],x] - 4*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_2 x+c_3 e^x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + 5*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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