15.14.11 problem 11

Internal problem ID [3183]
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 : 11
Date solved : Tuesday, March 04, 2025 at 04:05:05 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 45

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

\[ y = \frac {\left (-3+25 c_2 \right ) \cos \left (2 x \right )}{25}+\frac {\left (-3 x +20 c_4 \right ) \sin \left (2 x \right )}{20}+c_3 \,{\mathrm e}^{-x}+\frac {2 \,{\mathrm e}^{x} \left (x +\frac {5 c_{1}}{2}-\frac {9}{10}\right )}{5} \]

✓ Mathematica. Time used: 0.192 (sec). Leaf size: 55

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

\[ y(x)\to \frac {2 e^x x}{5}-\frac {9 e^x}{25}-\frac {\cos (x)}{2}+c_3 e^{-x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{3} e^{- x} + C_{4} \cos {\left (2 x \right )} + \left (C_{1} - \frac {3 x}{20}\right ) \sin {\left (2 x \right )} + \left (C_{2} + \frac {2 x}{5}\right ) e^{x} \]