80.8.12 problem 15

Internal problem ID [18591]
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 : Tuesday, January 28, 2025 at 12:03:23 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 x^{\prime } t +16 x&=\cos \left (3 \ln \left (t \right )\right ) \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[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]],x[t],t,IncludeSingularSolutions -> True]
 

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