89.7.28 problem 27

Internal problem ID [24459]
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 : 27
Date solved : Thursday, October 02, 2025 at 10:38:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 21

ode:=2*y(x)^3-x^3+3*x*y(x)^2*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {5^{{2}/{3}} {\left (\left (x^{5}+4\right ) x \right )}^{{1}/{3}}}{5 x} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 25

ode=( 2*y[x]^3-x^3)+(3*x*y[x]^2)*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sqrt [3]{x^5+4}}{\sqrt [3]{5} x^{2/3}} \end{align*}

✓ Sympy. Time used: 1.025 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + 3*x*y(x)**2*Derivative(y(x), x) + 2*y(x)**3,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {5^{\frac {2}{3}} \sqrt [3]{x^{3} + \frac {4}{x^{2}}}}{5} \]