29.18.35 problem 513

Internal problem ID [5109]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 513
Date solved : Sunday, March 30, 2025 at 06:40:56 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }&=a \,x^{n}+b y^{2} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 84

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

\begin{align*} y &= \frac {\sqrt {-4 \left (b -\frac {n}{2}\right ) \left (-\left (b -\frac {n}{2}\right ) c_1 \,x^{2 b}+a \,x^{n}\right )}}{2 b -n} \\ y &= -\frac {\sqrt {-4 \left (b -\frac {n}{2}\right ) \left (-\left (b -\frac {n}{2}\right ) c_1 \,x^{2 b}+a \,x^{n}\right )}}{2 b -n} \\ \end{align*}

✓ Mathematica. Time used: 4.793 (sec). Leaf size: 86

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

\begin{align*} y(x)\to -\frac {\sqrt {-2 a x^n+c_1 (2 b-n) x^{2 b}}}{\sqrt {2 b-n}} \\ y(x)\to \frac {\sqrt {-2 a x^n+c_1 (2 b-n) x^{2 b}}}{\sqrt {2 b-n}} \\ \end{align*}

✗ Sympy

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

Timed Out