53.1.11 problem 11

Internal problem ID [8445]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES Page 309
Problem number : 11
Date solved : Wednesday, March 05, 2025 at 05:48:01 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (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 &= -\frac {2}{x^{2}-2 c_{1}} \\ y &= c_{1} {\mathrm e}^{\frac {x^{3}}{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.163 (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: 0.413 (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)
 

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