85.37.7 problem 2 (a)

Internal problem ID [22750]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 175
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 09:14:19 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.052 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -3} 
dsolve(ode,func=y(x),ics=ics)
 

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