87.3.10 problem 10

Internal problem ID [23259]
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 1. Elementary methods. First order differential equations. Exercise at page 26
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:27:18 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \frac {c_1}{\left (x^{2}+4\right )^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {c_1}{\left (x^2+4\right )^{3/2}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {C_{1}}{\left (x^{2} + 4\right )^{\frac {3}{2}}} \]