56.5.17 problem 17

Internal problem ID [8978]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 07:13:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=5 \end{align*}

✓ Maple. Time used: 1.192 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-4*y(t) = 6*exp(-2+2*t); 
ic:=y(1) = 4, D(y)(1) = 5; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 3 \,{\mathrm e}^{t -1}+{\mathrm e}^{2 t -2} \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.240 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*y(t) - 6*exp(2*t - 2) + 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(1): 4, Subs(Derivative(y(t), t), t, 1): 5} 
dsolve(ode,func=y(t),ics=ics)
 

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