29.20.17 problem 564

Internal problem ID [5158]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 564
Date solved : Sunday, March 30, 2025 at 06:46:02 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 107

ode:=x*(x^n+a*y(x))*diff(y(x),x)+(b+c*y(x))*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {b}{\operatorname {RootOf}\left (-\textit {\_Z}^{\frac {a n}{b}} x^{-n} a^{2} b n -\textit {\_Z}^{\frac {a n}{b}} x^{-n} a \,b^{2}+c_1 \,a^{2} n^{2}+\textit {\_Z}^{\frac {a n}{b}} a c n -\textit {\_Z}^{\frac {a n +b}{b}} a n b +c_1 a b n +\textit {\_Z}^{\frac {a n}{b}} b c \right ) b -c} \]

✓ Mathematica. Time used: 1.96 (sec). Leaf size: 91

ode=x(x^n+a y[x])D[y[x],x]+(b+c y[x])y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)^{-\frac {a n+b}{b}} (c y(x)-a n) (b+c y(x))^{\frac {a n}{b}}}{a^2 n^2 (a n+b)}-\frac {x^{-n} e^{-\frac {a n (\log (y(x))-\log (b+c y(x)))}{b}}}{a n^2}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
n = symbols("n") 
y = Function("y") 
ode = Eq(x*(a*y(x) + x**n)*Derivative(y(x), x) + (b + c*y(x))*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out