73.20.10 problem 29.7 (e)

Internal problem ID [15619]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 29. Convolution. Additional Exercises. page 523
Problem number : 29.7 (e)
Date solved : Tuesday, January 28, 2025 at 08:03:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \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: 8.565 (sec). Leaf size: 20

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

\[ y = \frac {{\mathrm e}^{t}}{4}+\frac {\left (2 t -1\right ) {\mathrm e}^{3 t}}{4} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 68

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

\[ y(t)\to -e^{3 t} \int _1^0-e^{-2 K[1]} K[1]dK[1]+e^{3 t} \int _1^t-e^{-2 K[1]} K[1]dK[1]+\frac {1}{2} e^t \left (e^{2 t}-1\right ) t \]