74.12.13 problem 13

Internal problem ID [16320]
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 : Tuesday, January 28, 2025 at 09:03:59 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*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+34*y(t)=exp(3*t)*tan(5*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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