72.16.26 problem 27

Internal problem ID [14922]
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 : 27
Date solved : Tuesday, January 28, 2025 at 07:20:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y&=-3 \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: 0.019 (sec). Leaf size: 14

dsolve([diff(y(t),t$2)+2*y(t)=-3,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]+2*y[t]==-3,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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