54.4.25 problem 28

Internal problem ID [8609]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots Nonintegral. Exercises page 365
Problem number : 28
Date solved : Wednesday, March 05, 2025 at 06:10:33 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=2*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{{5}/{2}} c_{2} +c_{1}}{x^{2}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 x^{5/2}+c_1}{x^2} \]

✓ Sympy. Time used: 0.155 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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