87.9.20 problem 35

Internal problem ID [23393]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 74
Problem number : 35
Date solved : Thursday, October 02, 2025 at 09:40:59 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }-3 y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=x*diff(diff(y(x),x),x)-3*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2} \operatorname {BesselI}\left (4, 2 \sqrt {5}\, \sqrt {x}\right )+c_2 \,x^{2} \operatorname {BesselK}\left (4, 2 \sqrt {5}\, \sqrt {x}\right ) \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 46

ode=x*D[y[x],{x,2}]-3*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 50 x^2 \left (12 c_1 \operatorname {BesselI}\left (4,2 \sqrt {5} \sqrt {x}\right )+c_2 K_4\left (2 \sqrt {5} \sqrt {x}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - 5*y(x) - 3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} I_{4}\left (2 \sqrt {5} \sqrt {x}\right ) + C_{2} Y_{4}\left (2 \sqrt {5} i \sqrt {x}\right )\right ) \]