77.1.30 problem 47 (page 56)

Internal problem ID [17849]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 47 (page 56)
Date solved : Monday, March 31, 2025 at 04:36:08 PM
CAS classification : [_rational]

\begin{align*} y^{\prime } \left (x^{2}+y^{2}+3\right )&=2 x \left (2 y-\frac {x^{2}}{y}\right ) \end{align*}

✓ Maple. Time used: 0.170 (sec). Leaf size: 3277

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.202 (sec). Leaf size: 2419

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

Too large to display

✗ Sympy

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

Timed Out