73.19.5 problem 28.8 (b)

Internal problem ID [15603]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number : 28.8 (b)
Date solved : Tuesday, January 28, 2025 at 08:03:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 t} t^{2} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.785 (sec). Leaf size: 13

dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=exp(3*t)*t^2,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {t^{4} {\mathrm e}^{3 t}}{12} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==Exp[3*t]*t^2,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{12} e^{3 t} t^4 \]