Internal problem ID [12900]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=-\cos \left (\frac {t}{2}\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(t),t$2)+4*y(t)=-cos(t/2),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )-\frac {4 \cos \left (\frac {t}{2}\right )}{15} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 30
DSolve[y''[t]+4*y[t]==-Cos[t/2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {4}{15} \cos \left (\frac {t}{2}\right )+c_1 \cos (2 t)+c_2 \sin (2 t) \]