15.5.7 problem 7

Internal problem ID [2943]
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 : 7
Date solved : Sunday, March 30, 2025 at 01:00:29 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.164 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.196 (sec). Leaf size: 10

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

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