Internal problem ID [14527]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\cos \left (2 t \right )+t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(t),t$2)+4*y(t)=cos(2*t)+t,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (8 c_{1} +1\right ) \cos \left (2 t \right )}{8}+\frac {\left (8 c_{2} +2 t \right ) \sin \left (2 t \right )}{8}+\frac {t}{4} \]
✓ Solution by Mathematica
Time used: 0.223 (sec). Leaf size: 36
DSolve[y''[t]+4*y[t]==Cos[2*t]+t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} ((1+8 c_1) \cos (2 t)+2 (t+(t+4 c_2) \sin (2 t))) \]