14.7.6 problem 6

Internal problem ID [2550]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 6
Date solved : Sunday, March 30, 2025 at 12:09:54 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.086 (sec). Leaf size: 21

ode:=2*diff(diff(y(t),t),t)+diff(y(t),t)-10*y(t) = 0; 
ic:=y(1) = 5, D(y)(1) = 2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {16 \,{\mathrm e}^{\frac {5}{2}-\frac {5 t}{2}}}{9}+\frac {29 \,{\mathrm e}^{-2+2 t}}{9} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 30

ode=2*D[y[t],{t,2}]+D[y[t],t]-10*y[t]==0; 
ic={y[1]==5,Derivative[1][y][1] ==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {16}{9} e^{-\frac {5}{2} (t-1)}+\frac {29}{9} e^{2 t-2} \]

✓ Sympy. Time used: 0.166 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-10*y(t) + Derivative(y(t), t) + 2*Derivative(y(t), (t, 2)),0) 
ics = {y(1): 5, Subs(Derivative(y(t), t), t, 1): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {29 e^{2 t}}{9 e^{2}} + \frac {16 e^{\frac {5}{2}} e^{- \frac {5 t}{2}}}{9} \]