15.14.27 problem 27

Internal problem ID [3199]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 27
Date solved : Tuesday, March 04, 2025 at 04:05:47 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y&=\sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 6182

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

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 1.926 (sec). Leaf size: 1124

ode=D[y[x],{x,4}]+3*D[y[x],{x,2}]-D[y[x],x]+2*y[x]==Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -2*y(x) + sin(2*x) + Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) - Derivative(y(x), (x, 4)) cannot be solved by the factorable group method