87.11.30 problem 30

Internal problem ID [23448]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 84
Problem number : 30
Date solved : Thursday, October 02, 2025 at 09:41:53 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+13*diff(diff(y(x),x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (2 x \right )+c_2 \cos \left (2 x \right )+c_3 \sin \left (3 x \right )+c_4 \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode=D[y[x],{x,4}]+13*D[y[x],{x,2}]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 \cos (2 x)+c_1 \cos (3 x)+c_4 \sin (2 x)+c_2 \sin (3 x) \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) + 13*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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