10.7.17 problem 19

Internal problem ID [1265]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 19
Date solved : Saturday, March 29, 2025 at 10:50:38 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 )&={\frac {5}{4}}\\ y^{\prime }\left (0\right )&=-{\frac {3}{4}} \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-y(x) = 0; 
ic:=y(0) = 5/4, D(y)(0) = -3/4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x}+\frac {{\mathrm e}^{x}}{4} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-y[x]==0; 
ic={y[0]==5/4,Derivative[1][y][0] ==-3/4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x}+\frac {e^x}{4} \]

✓ Sympy. Time used: 0.067 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 5/4, Subs(Derivative(y(x), x), x, 0): -3/4} 
dsolve(ode,func=y(x),ics=ics)
 

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