72.16.33 problem 34

Internal problem ID [14929]
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 : 34
Date solved : Tuesday, January 28, 2025 at 07:20:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t^{2} \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: 0.016 (sec). Leaf size: 26

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

\[ y = \frac {7}{4}-\frac {3 t}{2}+\frac {t^{2}}{2}+\frac {{\mathrm e}^{-2 t}}{4}-2 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 37

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

\[ y(t)\to \frac {1}{4} e^{-2 t} \left (e^{2 t} \left (2 t^2-6 t+7\right )-8 e^t+1\right ) \]