86.11.9 problem 9

Internal problem ID [23203]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 9. The operational method. Exercise 9c at page 137
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:24:19 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-4*y(x) = 12; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} c_2 +{\mathrm e}^{2 x} c_1 -3 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to c_1 e^{2 x}+c_2 e^{-2 x}-3 \end{align*}

✓ Sympy. Time used: 0.044 (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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{2 x} - 3 \]