87.13.10 problem 10

Internal problem ID [23493]
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 100
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:42:24 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)+7/2*x*diff(y(x),x)-3/2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sqrt {x}+\frac {c_2}{x^{3}} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

ode=x^2*D[y[x],{x,2}]+7/2*x*D[y[x],x]-3/2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x^{7/2}+c_1}{x^3} \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x)/2 - 3*y(x)/2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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