61.4.14 problem Problem 2(l)[n]

Internal problem ID [15339]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 2(l)[n]
Date solved : Thursday, October 02, 2025 at 10:11:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.094 (sec). Leaf size: 18

ode:=3*diff(diff(y(t),t),t)+5*diff(y(t),t)-2*y(t) = 7*exp(-2*t); 
ic:=[y(0) = 3, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 23

ode=3*D[y[t],{t,2}]+5*D[y[t],t]-2*y[t]==7*Exp[-2*t]; 
ic={y[0]==3,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 3 e^{t/3}-e^{-2 t} t \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) + 5*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) - 7*exp(-2*t),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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