74.12.13 problem 13

Internal problem ID [16241]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 13
Date solved : Thursday, March 13, 2025 at 08:04:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 41

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+34*y(t) = exp(3*t)*tan(5*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{3 t} \left (25 \sin \left (5 t \right ) c_{2} -\ln \left (\sec \left (5 t \right )+\tan \left (5 t \right )\right ) \cos \left (5 t \right )+25 \cos \left (5 t \right ) c_{1} \right )}{25} \]

✓ Mathematica. Time used: 0.329 (sec). Leaf size: 108

ode=D[y[t],{t,2}]-6*D[y[t],t]+4*y[t]==Exp[3*t]*Tan[5*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-\left (\left (\sqrt {5}-3\right ) t\right )} \left (\int _1^t-\frac {e^{\sqrt {5} K[1]} \tan (5 K[1])}{2 \sqrt {5}}dK[1]+e^{2 \sqrt {5} t} \int _1^t\frac {e^{-\sqrt {5} K[2]} \tan (5 K[2])}{2 \sqrt {5}}dK[2]+c_2 e^{2 \sqrt {5} t}+c_1\right ) \]

✓ Sympy. Time used: 0.547 (sec). Leaf size: 41

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(34*y(t) - exp(3*t)*tan(5*t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{2} \sin {\left (5 t \right )} + \left (C_{1} + \frac {\log {\left (\sin {\left (5 t \right )} - 1 \right )}}{50} - \frac {\log {\left (\sin {\left (5 t \right )} + 1 \right )}}{50}\right ) \cos {\left (5 t \right )}\right ) e^{3 t} \]