74.12.14 problem 14

Internal problem ID [16321]
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 : 14
Date solved : Tuesday, January 28, 2025 at 09:04:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&={\mathrm e}^{5 t} \cot \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 42

dsolve(diff(y(t),t$2)-10*diff(y(t),t)+34*y(t)=exp(5*t)*cot(3*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{5 t} \left (\ln \left (\csc \left (3 t \right )-\cot \left (3 t \right )\right ) \sin \left (3 t \right )+9 \sin \left (3 t \right ) c_{2} +9 \cos \left (3 t \right ) c_{1} \right )}{9} \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 73

DSolve[D[y[t],{t,2}]-10*D[y[t],t]+34*y[t]==Exp[5*t]*Cot[3*t],y[t],t,IncludeSingularSolutions -> True]
 

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