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 : Wednesday, March 05, 2025 at 04:24:01 AM
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*}

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

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-4*y(t) = 6*exp(2*t-3); 
ic:=y(3/2) = 4, D(y)(3/2) = 5; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.286 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*y(t) - 6*exp(2*t - 3) + 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(3/2): 4, Subs(Derivative(y(t), t), t, 3/2): 5} 
dsolve(ode,func=y(t),ics=ics)
 

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