2.7.29 problem 54

Internal problem ID [835]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 54
Date solved : Tuesday, September 30, 2025 at 04:15:57 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y&=0 \end{align*}

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

ode:=4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}+c_2}{x^{{3}/{2}}} \]

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

ode=4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]-3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.119 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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