49.6.9 problem 1(i)

Internal problem ID [7637]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 69
Problem number : 1(i)
Date solved : Sunday, March 30, 2025 at 12:17:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 33

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

\[ y(x)\to \frac {e^x}{3}+c_1 e^{x/2}+c_2 e^{-x/2} \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 20

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

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