74.12.11 problem 11

Internal problem ID [16318]
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 : 11
Date solved : Tuesday, January 28, 2025 at 09:03:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+26 y&={\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 52

dsolve(diff(y(t),t$2)-2*diff(y(t),t)+26*y(t)=exp(t)*(sec(5*t)+csc(5*t)),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 50

DSolve[D[y[t],{t,2}]-2*D[y[t],t]+26*y[t]==Exp[t]*(Sec[5*t]+Csc[5*t]),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{25} e^t (\cos (5 t) (-5 t+\log (\cos (5 t))+25 c_2)+\sin (5 t) (\log (\sin (5 t))+5 (t+5 c_1))) \]