73.10.16 problem 15.6 (c)

Internal problem ID [15232]
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 : 15.6 (c)
Date solved : Thursday, March 13, 2025 at 05:50:09 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=-24 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+9*y(x) = 0; 
ic:=y(0) = 8, D(y)(0) = -24; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 12 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{9 x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 17

ode=D[y[x],{x,2}]-10*D[y[x],x]+9*y[x]==0; 
ic={y[0]==8,Derivative[1][y][0] ==-24}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -4 e^x \left (e^{8 x}-3\right ) \]

✓ Sympy. Time used: 0.183 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 8, Subs(Derivative(y(x), x), x, 0): -24} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (12 - 4 e^{8 x}\right ) e^{x} \]