46.6.9 problem 9

Internal problem ID [7355]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:50:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8 \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: 0.224 (sec). Leaf size: 16

dsolve([diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=6*t-8,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 2 t -2 \,{\mathrm e}^{2 t} \sinh \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==6*t-8,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 t+e^t-e^{3 t} \]