7.9.10 problem 22

Internal problem ID [258]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 22
Date solved : Tuesday, March 04, 2025 at 11:06:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y&=12 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=10 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-4*y(x) = 12; 
ic:=y(0) = 0, D(y)(0) = 10; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 21

ode=D[y[x],{x,2}]-4*y[x]==12; 
ic={y[0]==0,Derivative[1][y][0] ==10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.098 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), (x, 2)) - 12,0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 10} 
dsolve(ode,func=y(x),ics=ics)
 

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