Internal problem ID [13221]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.3 page 424
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=3 \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(t),t$2)+4*y(t)=3*cos(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (6 t +8 c_{2} \right ) \sin \left (2 t \right )}{8}+\frac {\left (8 c_{1} +3\right ) \cos \left (2 t \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 33
DSolve[y''[t]+4*y[t]==3*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (\frac {3}{16}+c_1\right ) \cos (2 t)+\frac {1}{4} (3 t+4 c_2) \sin (2 t) \]