89.7.10 problem 10

Internal problem ID [24441]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:32:22 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 43

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

\begin{align*} y &= \frac {\sqrt {\left (-x +c_1 \right ) x}\, x}{-x +c_1} \\ y &= \frac {\sqrt {\left (-x +c_1 \right ) x}\, x}{-c_1 +x} \\ \end{align*}

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.433 (sec). Leaf size: 26

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

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