61.5.8 problem Problem 2(c)

Internal problem ID [15375]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 2(c)
Date solved : Thursday, October 02, 2025 at 10:12:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-7 y&=4 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)-7*y(t) = 4; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{\frac {\left (3+\sqrt {37}\right ) t}{2}} c_2 +{\mathrm e}^{-\frac {\left (-3+\sqrt {37}\right ) t}{2}} c_1 -\frac {4}{7} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 43

ode=D[y[t],{t,2}]-3*D[y[t],t]-7*y[t]==4; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{-\frac {1}{2} \left (\sqrt {37}-3\right ) t}+c_2 e^{\frac {1}{2} \left (3+\sqrt {37}\right ) t}-\frac {4}{7} \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-7*y(t) - 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 4,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{\frac {t \left (3 - \sqrt {37}\right )}{2}} + C_{2} e^{\frac {t \left (3 + \sqrt {37}\right )}{2}} - \frac {4}{7} \]