30.3.18 problem 19

Internal problem ID [7474]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 04:37:23 PM
CAS classification : [_exact, _rational]

\begin{align*} 2 x +\frac {y}{1+x^{2} y^{2}}+\left (\frac {x}{1+x^{2} y^{2}}-2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 32

ode:=2*x+y(x)/(1+x^2*y(x)^2)+(x/(1+x^2*y(x)^2)-2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\tan \left (\operatorname {RootOf}\left (x^{4}+c_1 \,x^{2}-x^{2} \textit {\_Z} -\tan \left (\textit {\_Z} \right )^{2}\right )\right )}{x} \]

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 23

ode=( 2*x + y[x]/(1+x^2*y[x]^2))+( x/(1+x^2*y[x]^2)-2*y[x] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\arctan (x y(x))-x^2+y(x)^2=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (x/(x**2*y(x)**2 + 1) - 2*y(x))*Derivative(y(x), x) + y(x)/(x**2*y(x)**2 + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out