88.14.6 problem 6

Internal problem ID [24094]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 93
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:59:11 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 34

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 49

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

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

✓ Sympy. Time used: 0.108 (sec). Leaf size: 42

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

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