15.14.10 problem 10

Internal problem ID [3182]
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 : 10
Date solved : Sunday, March 30, 2025 at 01:20:36 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 41

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

\[ y = \frac {\left (8-17 x +289 c_3 \right ) {\mathrm e}^{4 x}}{289}+\frac {\left (578 c_1 +68 x +15\right ) \cos \left (x \right )}{578}-\frac {\sin \left (x \right ) \left (x -34 c_2 +\frac {8}{17}\right )}{34} \]

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 52

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

\[ y(x)\to \frac {1}{289} e^{4 x} (-17 x+8+289 c_3)+\left (\frac {2 x}{17}+\frac {13}{1156}+c_1\right ) \cos (x)+\left (-\frac {x}{34}-\frac {21}{289}+c_2\right ) \sin (x) \]

✓ Sympy. Time used: 0.253 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = \left (C_{1} - \frac {x}{17}\right ) e^{4 x} + \left (C_{2} - \frac {x}{34}\right ) \sin {\left (x \right )} + \left (C_{3} + \frac {2 x}{17}\right ) \cos {\left (x \right )} \]