73.18.8 problem 27.1 (h)

Internal problem ID [15592]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.1 (h)
Date solved : Tuesday, January 28, 2025 at 08:02:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 9.133 (sec). Leaf size: 20

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=exp(4*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{7 t}+119 \,{\mathrm e}^{t}-78\right ) {\mathrm e}^{-3 t}}{42} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+6*y[t]==Exp[4*t],{y[0]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{42} e^{-3 t} \left (119 e^t+e^{7 t}-78\right ) \]