15.9.30 problem 44

Internal problem ID [3087]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 44
Date solved : Tuesday, March 04, 2025 at 03:58:26 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\[ y = c_{1} +c_2 \sin \left (\sqrt {2}\, x \right )+c_3 \cos \left (\sqrt {2}\, x \right )+c_4 \sin \left (x \right )+c_5 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 52

ode=D[y[x],{x,5}]+3*D[y[x],{x,3}]+2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -c_4 \cos (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \sin (x)+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_5 \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (x \right )} + C_{3} \sin {\left (\sqrt {2} x \right )} + C_{4} \cos {\left (x \right )} + C_{5} \cos {\left (\sqrt {2} x \right )} \]