72.16.28 problem 29

Internal problem ID [14924]
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 4.1 page 399
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 07:20:43 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=6 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 12

dsolve([diff(y(t),t$2)+9*y(t)=6,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {2}{3}-\frac {2 \cos \left (3 t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]+9*y[t]==6,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {4}{3} \sin ^2\left (\frac {3 t}{2}\right ) \]