72.16.30 problem 31

Internal problem ID [14926]
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 : 31
Date solved : Tuesday, January 28, 2025 at 07:20:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y&=-3 t^{2}+2 t +3 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 26

dsolve([diff(y(t),t$2)+4*y(t)=-3*t^2+2*t+3,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {\sin \left (2 t \right )}{4}+\frac {7 \cos \left (2 t \right )}{8}-\frac {3 t^{2}}{4}+\frac {t}{2}+\frac {9}{8} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 31

DSolve[{D[y[t],{t,2}]+4*y[t]==-3*t^2+2*t+3,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{8} \left (-6 t^2+4 t-2 \sin (2 t)-9 \cos (2 t)+9\right ) \]