67.10.3 problem 15.2 (c)

Internal problem ID [16585]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (c)
Date solved : Thursday, October 02, 2025 at 01:36:39 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=8 \\ y^{\prime }\left (0\right )&=-9 \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-6*y(x) = 0; 
ic:=[y(0) = 8, D(y)(0) = -9]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{-3 x}+3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 20

ode=D[y[x],{x,2}]+D[y[x],x]-6*y[x]==0; 
ic={y[0]==8,Derivative[1][y][0] ==-9}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (3 e^{5 x}+5\right ) \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 8, Subs(Derivative(y(x), x), x, 0): -9} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 e^{2 x} + 5 e^{- 3 x} \]