87.9.27 problem 42

Internal problem ID [23400]
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 74
Problem number : 42
Date solved : Thursday, October 02, 2025 at 09:41:05 PM
CAS classification : [[_2nd_order, _missing_y]]

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

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

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 17

ode=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 c_2-\frac {c_1}{3 x^3} \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 8

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

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