23.2.9 problem 4(i)

Internal problem ID [4126]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 4(i)
Date solved : Sunday, March 30, 2025 at 02:40:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=4*diff(diff(y(x),x),x)+diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x}{8}} \left (c_1 \sin \left (\frac {\sqrt {15}\, x}{8}\right )+c_2 \cos \left (\frac {\sqrt {15}\, x}{8}\right )\right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 42

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

\[ y(x)\to e^{-x/8} \left (c_2 \cos \left (\frac {\sqrt {15} x}{8}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{8}\right )\right ) \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {15} x}{8} \right )} + C_{2} \cos {\left (\frac {\sqrt {15} x}{8} \right )}\right ) e^{- \frac {x}{8}} \]