2.8.3 problem 23

Internal problem ID [840]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 04:16:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=11 \\ \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x) = 6; 
ic:=[y(0) = 3, D(y)(0) = 11]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x}+4 \,{\mathrm e}^{3 x}-2 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 19

ode=D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==6; 
ic={y[0]==3,Derivative[1][y][0] ==11}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x}+4 e^{3 x}-2 \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 6,0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 11} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 4 e^{3 x} - 2 + e^{- x} \]