64.3.18 problem 24

Internal problem ID [13218]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 24
Date solved : Monday, March 31, 2025 at 07:39:45 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Maple. Time used: 0.051 (sec). Leaf size: 28

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

\[ y = x \cot \left (\operatorname {RootOf}\left (4 c_1 \sin \left (\textit {\_Z} \right )^{4}-4 \textit {\_Z} \sin \left (\textit {\_Z} \right )^{4}-x^{4}\right )\right ) \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 116

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (K[2]^3+x^2 K[2]-\int _1^x\left (-\frac {2 K[2]^2}{\left (K[1]^2+K[2]^2\right )^2}+2 K[1] K[2]+\frac {1}{K[1]^2+K[2]^2}\right )dK[1]-\frac {x}{x^2+K[2]^2}\right )dK[2]+\int _1^x\left (K[1]^3+y(x)^2 K[1]+\frac {y(x)}{K[1]^2+y(x)^2}\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out