30.5.8 problem 8

Internal problem ID [7507]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:40:40 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\begin{align*} y &= 0 \\ y &= \frac {x^{{3}/{2}}}{c_1 x -\sqrt {x}} \\ \end{align*}

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.186 (sec). Leaf size: 15

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

\[ \left [ y{\left (x \right )} = \frac {x}{C_{1} \sqrt {x} - 1}, \ y{\left (x \right )} = 0\right ] \]