83.8.17 problem 18

Internal problem ID [19072]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 18
Date solved : Monday, March 31, 2025 at 06:43:29 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 21

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

\[ x +\frac {\ln \left (x^{2}+y^{2}\right )}{2}-2 y+c_1 = 0 \]

✓ Mathematica. Time used: 0.201 (sec). Leaf size: 27

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

\[ \text {Solve}\left [-\frac {1}{2} \log \left (x^2+y(x)^2\right )+2 y(x)-x=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out