29.36.16 problem 1084

Internal problem ID [5643]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1084
Date solved : Sunday, March 30, 2025 at 09:46:40 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.297 (sec). Leaf size: 341

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

\begin{align*} y &= -\frac {\sqrt {-6-81 x^{2}-6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y &= \frac {\sqrt {-6-81 x^{2}-6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y &= -\frac {\sqrt {-6-81 x^{2}+6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y &= \frac {\sqrt {-6-81 x^{2}+6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y &= \sqrt {-\left (c_1^{3}\right )^{{2}/{3}}+2 c_1 x +c_1^{3}-x^{2}} \\ y &= -\sqrt {-\left (c_1^{3}\right )^{{2}/{3}}+2 c_1 x +c_1^{3}-x^{2}} \\ y &= -\frac {\sqrt {\left (-2 i \sqrt {3}+2\right ) \left (c_1^{3}\right )^{{2}/{3}}-4 i \sqrt {3}\, c_1 x +4 c_1^{3}-4 x^{2}-4 c_1 x}}{2} \\ y &= \frac {\sqrt {\left (-2 i \sqrt {3}+2\right ) \left (c_1^{3}\right )^{{2}/{3}}-4 i \sqrt {3}\, c_1 x +4 c_1^{3}-4 x^{2}-4 c_1 x}}{2} \\ y &= -\frac {\sqrt {\left (2 i \sqrt {3}+2\right ) \left (c_1^{3}\right )^{{2}/{3}}+4 i \sqrt {3}\, c_1 x +4 c_1^{3}-4 x^{2}-4 c_1 x}}{2} \\ y &= \frac {\sqrt {\left (2 i \sqrt {3}+2\right ) \left (c_1^{3}\right )^{{2}/{3}}+4 i \sqrt {3}\, c_1 x +4 c_1^{3}-4 x^{2}-4 c_1 x}}{2} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

IndexError : list index out of range