20.21.13 problem Problem 13

Internal problem ID [3940]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 13
Date solved : Tuesday, March 04, 2025 at 05:19:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 2.647 (sec). Leaf size: 21

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

\[ y = 2 \,{\mathrm e}^{t}+2 \,{\mathrm e}^{3 t}-4 \,{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 17

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

\[ y(t)\to 2 e^t \left (e^t-1\right )^2 \]

✓ Sympy. Time used: 0.208 (sec). Leaf size: 19

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

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