78.10.8 problem 6 (d)

Internal problem ID [18198]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 6 (d)
Date solved : Monday, March 31, 2025 at 05:22:32 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 16

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

\[ y(x)\to \frac {1}{e^2}-e^{-x} \]

✓ Sympy. Time used: 0.135 (sec). Leaf size: 12

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

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