23.5.42 problem 42

Internal problem ID [6651]
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 : 42
Date solved : Tuesday, September 30, 2025 at 03:50:32 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y-3 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=4*y(x)-3*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 27

ode=4*y[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 e^{-x} \left (e^{3 x} (c_3 x+c_2)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.051 (sec). Leaf size: 17

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

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