78.12.26 problem 5 (b)

Internal problem ID [18234]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 5 (b)
Date solved : Thursday, March 13, 2025 at 11:50:08 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=2*x^2*diff(diff(y(x),x),x)+10*x*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{2} \ln \left (x \right )+c_{1}}{x^{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 18

ode=2*x^2*D[y[x],{x,2}] +10*x*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 c_2 \log (x)+c_1}{x^2} \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 10*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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