23.1.398 problem 383

Internal problem ID [5005]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 383
Date solved : Sunday, October 12, 2025 at 01:21:14 AM
CAS classification : [_rational, _Abel]

\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 78

ode:=x^7*diff(y(x),x)+5*x^3*y(x)^2+2*(x^2+1)*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 +\frac {x}{\left (\frac {x^{6}+x^{2} y^{2}+2 y x^{3}+y^{2}}{x^{2} y^{2}}\right )^{{1}/{4}}}+\frac {\left (x^{3}+y\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x^{3}+y\right )^{2}}{x^{2} y^{2}}\right )}{2 x y} = 0 \]

✓ Mathematica. Time used: 0.192 (sec). Leaf size: 123

ode=x^7*D[y[x],x]+5*x^3*y[x]^2+2*(1+x^2)*y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \sqrt [4]{1-\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2} \left (\frac {i x^2}{y(x)}+\frac {i}{x}\right ) \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{4},\frac {3}{2},\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2}},y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**7*Derivative(y(x), x) + 5*x**3*y(x)**2 + (2*x**2 + 2)*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded