23.3.6 problem 7(f)

Internal problem ID [4147]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(f)
Date solved : Sunday, March 30, 2025 at 02:41:00 AM
CAS classification : [[_3rd_order, _missing_x]]

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

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

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

\[ y = c_1 +c_2 \sin \left (2 x \right )+c_3 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {1}{2} c_2 \cos (2 x)+c_1 \sin (x) \cos (x)+c_3 \]

✓ Sympy. Time used: 0.124 (sec). Leaf size: 17

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

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