89.28.11 problem 11

Internal problem ID [24899]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 229
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:49:13 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

\begin{align*} y &= c_1 \,{\mathrm e}^{\frac {x^{3}}{3}} \\ y &= -\frac {2}{x^{2}-2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.238 (sec). Leaf size: 20

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

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