85.46.3 problem 3

Internal problem ID [22791]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 181
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:14:40 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 52

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

\[ y = c_1 \,{\mathrm e}^{2^{{2}/{3}} x}-c_2 \,{\mathrm e}^{-\frac {2^{{2}/{3}} x}{2}} \sin \left (\frac {\sqrt {3}\, 2^{{2}/{3}} x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {2^{{2}/{3}} x}{2}} \cos \left (\frac {\sqrt {3}\, 2^{{2}/{3}} x}{2}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 62

ode=D[y[x],{x,3}]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\frac {x}{\sqrt [3]{2}}} \left (c_3 e^{\frac {3 x}{\sqrt [3]{2}}}+c_1 \cos \left (\frac {\sqrt {3} x}{\sqrt [3]{2}}\right )+c_2 \sin \left (\frac {\sqrt {3} x}{\sqrt [3]{2}}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 56

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

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