80.8.12 problem 15

Internal problem ID [18512]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 15
Date solved : Thursday, March 13, 2025 at 12:11:23 PM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x&=\cos \left (3 \ln \left (t \right )\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 43

ode:=t^4*diff(diff(diff(diff(x(t),t),t),t),t)-2*t^3*diff(diff(diff(x(t),t),t),t)-20*t^2*diff(diff(x(t),t),t)+12*t*diff(x(t),t)+16*x(t) = cos(3*ln(t)); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {\left (15066+34263 i\right ) t^{1-3 i}+\left (15066-34263 i\right ) t^{1+3 i}[phone] t^{9} c_3 -1281150 c_{2} t^{3}+854100 c_{1} \ln \left (t \right )+94900 c_{1} [phone] c_4}{23060700 t} \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 48

ode=t^4*D[x[t],{t,4}]-2*t^3*D[x[t],{t,3}]-20*t^2*D[x[t],{t,2}]+12*t*D[x[t],t]+16*x[t]==Cos[3*Log[t]]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {c_4 t^9+c_3 t^3+c_2 \log (t)+c_1}{t}+\frac {141 \sin (3 \log (t))}{47450}+\frac {31 \cos (3 \log (t))}{23725} \]

✓ Sympy. Time used: 0.718 (sec). Leaf size: 42

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**4*Derivative(x(t), (t, 4)) - 2*t**3*Derivative(x(t), (t, 3)) - 20*t**2*Derivative(x(t), (t, 2)) + 12*t*Derivative(x(t), t) + 16*x(t) - cos(3*log(t)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1}}{t} + C_{2} t^{2} + C_{3} t^{8} + \frac {C_{4} \log {\left (t \right )}}{t} + \frac {141 \sin {\left (3 \log {\left (t \right )} \right )}}{47450} + \frac {31 \cos {\left (3 \log {\left (t \right )} \right )}}{23725} \]