86.5.8 problem 8

Internal problem ID [23122]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5a at page 74
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:23:06 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-63 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-63*y(x) = 0; 
ic:=[y(0) = 5, D(y)(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {5 \,{\mathrm e}^{-7 x}}{2}+\frac {5 \,{\mathrm e}^{9 x}}{2} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 21

ode=D[y[x],{x,2}]-2*D[y[x],x]-63*y[x]==0; 
ic={y[0]==5,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5}{2} e^{-7 x} \left (e^{16 x}+1\right ) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-63*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 5, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {5 e^{9 x}}{2} + \frac {5 e^{- 7 x}}{2} \]