83.23.21 problem 21

Internal problem ID [19231]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 21
Date solved : Monday, March 31, 2025 at 06:59:30 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}&=y^{4} \left (y+x y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.339 (sec). Leaf size: 47

ode:=diff(y(x),x)^3 = y(x)^4*(x*diff(y(x),x)+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {3 \sqrt {3}}{2 x^{{3}/{2}}} \\ y &= \frac {3 \sqrt {3}}{2 x^{{3}/{2}}} \\ y &= 0 \\ y &= c_1 \sqrt {\frac {c_1^{10}}{\left (c_1^{4} x -1\right )^{2}}} \\ \end{align*}

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 64

ode=D[y[x],x]^3==y[x]^4*(y[x]+x*D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{c_1 x-c_1{}^3} \\ y(x)\to 0 \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\frac {3 \sqrt {3}}{2 x^{3/2}} \\ y(x)\to \frac {3 \sqrt {3}}{2 x^{3/2}} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x*Derivative(y(x), x) - y(x))*y(x)**4 + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out