72.18.3 problem 3

Internal problem ID [14956]
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
Date solved : Tuesday, January 28, 2025 at 07:25:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=-\cos \left (\frac {t}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(t),t$2)+4*y(t)=-cos(t/2),y(t), singsol=all)
 

\[ y = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} -\frac {4 \cos \left (\frac {t}{2}\right )}{15} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 30

DSolve[D[y[t],{t,2}]+4*y[t]==-Cos[t/2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {4}{15} \cos \left (\frac {t}{2}\right )+c_1 \cos (2 t)+c_2 \sin (2 t) \]