83.21.9 problem 9

Internal problem ID [19182]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (D) at page 57
Problem number : 9
Date solved : Monday, March 31, 2025 at 06:51:28 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.075 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 54

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

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

✗ Sympy

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

Timed Out