46.6.7 problem 7

Internal problem ID [7353]
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 : 7
Date solved : Monday, January 27, 2025 at 02:50:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {7}{2}}\\ y^{\prime }\left (0\right )&=-10 \end{align*}

✓ Solution by Maple

Time used: 0.253 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)+7*diff(y(t),t)+12*y(t)=21*exp(3*t),y(0) = 7/2, D(y)(0) = -10],y(t), singsol=all)
 

\[ y = \frac {5 \,{\mathrm e}^{-4 t}}{2}+\cosh \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 28

DSolve[{D[y[t],{t,2}]+7*D[y[t],t]+12*y[t]==21*Exp[3*t],{y[0]==32/10,Derivative[1][y][0] ==62/10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{10} e^{-4 t} \left (155 e^t+5 e^{7 t}-128\right ) \]