Internal problem ID [14589]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+34 y={\mathrm e}^{5 t} \cot \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \frac {{\mathrm e}^{5 t} \left (\ln \left (\csc \left (3 t \right )-\cot \left (3 t \right )\right ) \sin \left (3 t \right )+9 c_{2} \sin \left (3 t \right )+9 c_{1} \cos \left (3 t \right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 49
DSolve[y''[t]-10*y'[t]+34*y[t]==Exp[5*t]*Cot[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{9} e^{5 t} \left (9 c_2 \cos (3 t)+\sin (3 t) \left (\log \left (\sin \left (\frac {3 t}{2}\right )\right )-\log \left (\cos \left (\frac {3 t}{2}\right )\right )+9 c_1\right )\right ) \]