70.13.48 problem 57

Internal problem ID [18917]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 57
Date solved : Thursday, October 02, 2025 at 03:32:52 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y&=0 \end{align*}

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

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{7}+c_1}{x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]-6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.093 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) - 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x^{6} \]