Internal problem ID [14526]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=4 \cos \left (t \right )-\sin \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(t),t$2)+4*y(t)=4*cos(t)-sin(t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} +\frac {4 \cos \left (t \right )}{3}-\frac {\sin \left (t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 32
DSolve[y''[t]+4*y[t]==4*Cos[t]-Sin[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {\sin (t)}{3}+\frac {4 \cos (t)}{3}+c_1 \cos (2 t)+c_2 \sin (2 t) \]