83.43.3 problem Ex 4 page 7

Internal problem ID [19440]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 4 page 7
Date solved : Monday, March 31, 2025 at 07:13:52 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Maple. Time used: 0.131 (sec). Leaf size: 34

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

\[ y = x \cot \left (\operatorname {RootOf}\left (2 c_1 \,a^{2} \sin \left (\textit {\_Z} \right )^{2}-2 \textit {\_Z} \,a^{2} \sin \left (\textit {\_Z} \right )^{2}-x^{2}\right )\right ) \]

✓ Mathematica. Time used: 0.233 (sec). Leaf size: 33

ode=(x^3+x*y[x]^2+a^2*y[x])+(y[x]^3+y[x]*x^2-a^2*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

Timed Out