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 : Wednesday, March 05, 2025 at 04:23:54 AM
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*}

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

ode:=diff(diff(y(t),t),t)+7*diff(y(t),t)+12*y(t) = 21*exp(3*t); 
ic:=y(0) = 7/2, D(y)(0) = -10; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.269 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(12*y(t) - 21*exp(3*t) + 7*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 7/2, Subs(Derivative(y(t), t), t, 0): -10} 
dsolve(ode,func=y(t),ics=ics)
 

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