2.8.2 problem 22

Internal problem ID [839]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 04:16:00 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: 0.043 (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,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (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]
 

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

✓ Sympy. Time used: 0.062 (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)
 

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