2.7.7 problem 7

Internal problem ID [813]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 04:15:39 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ y^{\prime }\left (0\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
ic:=[y(0) = -2, D(y)(0) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 6-8 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 14

ode=D[y[x],{x,2}]+D[y[x],x]==0; 
ic={y[0]==-2,Derivative[1][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 6-8 e^{-x} \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -2, Subs(Derivative(y(x), x), x, 0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 6 - 8 e^{- x} \]