67.1.10 problem 2.2 (j)

Internal problem ID [16275]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (j)
Date solved : Thursday, October 02, 2025 at 10:45:16 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.075 (sec). Leaf size: 8

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

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