89.6.10 problem 10

Internal problem ID [24393]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:24:21 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {2 x}{2 c_1 \,x^{2}-3} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.124 (sec). Leaf size: 12

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

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