23.1.600 problem 593

Internal problem ID [5207]
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 : 593
Date solved : Sunday, October 12, 2025 at 01:23:23 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 120

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

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

✓ Mathematica. Time used: 0.226 (sec). Leaf size: 98

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

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

✗ Sympy

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

Timed Out