67.3.9 problem Problem 10

Internal problem ID [13956]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 10
Date solved : Monday, March 31, 2025 at 08:20:14 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.105 (sec). Leaf size: 12

ode:=4*diff(diff(y(t),t),t)-12*diff(y(t),t)+13*y(t) = 0; 
ic:=y(0) = 2, D(y)(0) = 3; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{\frac {3 t}{2}} \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 16

ode=4*D[y[t],{t,2}]-12*D[y[t],t]+13*y[t]==0; 
ic={y[0]==2,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 2 e^{3 t/2} \cos (t) \]

✓ Sympy. Time used: 0.206 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(13*y(t) - 12*Derivative(y(t), t) + 4*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

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