15.5.4 problem 4

Internal problem ID [2940]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 4
Date solved : Tuesday, March 04, 2025 at 03:34:22 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {3 x^{2}}{3 c_1 \,x^{3}-1} \]

✓ Mathematica. Time used: 0.181 (sec). Leaf size: 26

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

\begin{align*} y(x)\to \frac {3 x^2}{-1+3 c_1 x^3} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 14

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

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