87.8.12 problem 12

Internal problem ID [23366]
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 65
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:40:41 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 y-3 x y^{\prime \prime }+4 y^{\prime }&=0 \end{align*}

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

ode:=2*y(x)-3*x*diff(diff(y(x),x),x)+4*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{{7}/{6}} \operatorname {BesselI}\left (\frac {7}{3}, \frac {2 \sqrt {6}\, \sqrt {x}}{3}\right )+c_2 \,x^{{7}/{6}} \operatorname {BesselK}\left (\frac {7}{3}, \frac {2 \sqrt {6}\, \sqrt {x}}{3}\right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 77

ode=2*y[x]-3*x*D[y[x],{x,2}]+4*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{3} \sqrt [6]{\frac {2}{3}} x^{7/6} \left (c_1 \operatorname {Gamma}\left (-\frac {4}{3}\right ) \operatorname {BesselI}\left (-\frac {7}{3},2 \sqrt {\frac {2}{3}} \sqrt {x}\right )+\sqrt [3]{-1} c_2 \operatorname {Gamma}\left (\frac {10}{3}\right ) \operatorname {BesselI}\left (\frac {7}{3},2 \sqrt {\frac {2}{3}} \sqrt {x}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*Derivative(y(x), (x, 2)) + 2*y(x) + 4*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{\frac {7}{6}} \left (C_{1} J_{\frac {7}{3}}\left (\frac {2 \sqrt {6} i \sqrt {x}}{3}\right ) + C_{2} Y_{\frac {7}{3}}\left (\frac {2 \sqrt {6} i \sqrt {x}}{3}\right )\right ) \]