73.18.10 problem 27.1 (j)

Internal problem ID [15594]
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 (j)
Date solved : Tuesday, January 28, 2025 at 08:02:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=7 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 8.819 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=7,y(0) = 2, D(y)(0) = 4],y(t), singsol=all)
 

\[ y = \frac {7 \,{\mathrm e}^{3 t}}{3}+\frac {7}{6}-\frac {3 \,{\mathrm e}^{2 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 25

DSolve[{D[y[t],{t,2}]-5*D[y[t],t]+6*y[t]==7,{y[0]==2,Derivative[1][y][0] ==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{6} \left (-9 e^{2 t}+14 e^{3 t}+7\right ) \]