46.6.15 problem 15

Internal problem ID [7361]
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 : 15
Date solved : Monday, January 27, 2025 at 02:50:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (\frac {3}{2}\right )&=4\\ y^{\prime }\left (\frac {3}{2}\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.247 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+3*diff(y(t),t)-4*y(t)=6*exp(2*t-3),y(3/2) = 4, D(y)(3/2) = 5],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 22

DSolve[{D[y[t],{t,2}]+3*D[y[t],t]-4*y[t]==6*Exp[2*t-3],{y[15/10]==4,Derivative[1][y][15/10 ]==5}},y[t],t,IncludeSingularSolutions -> True]
 

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