78.10.7 problem 6 (c)

Internal problem ID [18197]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 6 (c)
Date solved : Monday, March 31, 2025 at 05:22:30 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=D[y[x],{x,2}] +5*D[y[x],x]+6*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (4 e^x-3\right ) \]

✓ Sympy. Time used: 0.174 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \left (4 - 3 e^{- x}\right ) e^{- 2 x} \]