85.19.4 problem 4

Internal problem ID [22561]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 52
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:51:30 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 22

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

\[ \left (y^{2}+x^{2}\right ) \sqrt {y^{2}+1}+c_1 = 0 \]

✓ Mathematica. Time used: 26.067 (sec). Leaf size: 2372

ode=( 2*x+2*x*y[x]^2 )+( x^2*y[x]+2*y[x]+3*y[x]^3 )*D[y[x],x]==0; 
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*y(x)**2 + 2*x + (x**2*y(x) + 3*y(x)**3 + 2*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out