Internal problem ID [14535]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+26 y=-338 t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+26*y(t)=-338*t,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} \sin \left (5 t \right ) c_{2} +{\mathrm e}^{-t} \cos \left (5 t \right ) c_{1} -13 t +1 \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 34
DSolve[y''[t]+2*y'[t]+26*y[t]==-338*t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -13 t+c_2 e^{-t} \cos (5 t)+c_1 e^{-t} \sin (5 t)+1 \]