89.11.24 problem 24

Internal problem ID [24549]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 24
Date solved : Thursday, October 02, 2025 at 10:46:02 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 )&=0 \\ y \left (1\right )&={\mathrm e}^{3} \\ \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-6*y(x) = 0; 
ic:=[y(0) = 0, y(1) = exp(3)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {csch}\left (\frac {5}{2}\right ) \sinh \left (\frac {5 x}{2}\right ) {\mathrm e}^{\frac {5}{2}+\frac {x}{2}} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 27

ode=D[y[x],{x,2}] -D[y[x],x] -6*y[x] ==0; 
ic={y[0]==0,y[1] ==Exp[3]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{5-2 x} \left (e^{5 x}-1\right )}{e^5-1} \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 29

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): 0, y(1): exp(3)} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{5} e^{3 x}}{-1 + e^{5}} - \frac {e^{5} e^{- 2 x}}{-1 + e^{5}} \]