15.11.26 problem 26

Internal problem ID [3136]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 26
Date solved : Sunday, March 30, 2025 at 01:19:19 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 50

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*y(x) = 5*exp(2*x)*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 \cos \left (x \right )+c_4 \sin \left (x \right )\right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{2 x} \left (24 \cos \left (3 x \right )-23 \sin \left (3 x \right )\right )}{1105}+{\mathrm e}^{x} \left (c_1 \cos \left (x \right )+c_2 \sin \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 64

ode=D[y[x],{x,4}]+4*y[x]==5*Exp[2*x]*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{2 x} (24 \cos (3 x)-23 \sin (3 x))}{1105}+c_1 e^{-x} \cos (x)+c_4 e^x \cos (x)+c_2 e^{-x} \sin (x)+c_3 e^x \sin (x) \]

✓ Sympy. Time used: 0.242 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 5*exp(2*x)*sin(3*x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{- x} + \left (C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (x \right )}\right ) e^{x} + \frac {\left (- 23 \sin {\left (3 x \right )} + 24 \cos {\left (3 x \right )}\right ) e^{2 x}}{1105} \]