2.294   ODE No. 294

x(a+x2+y(x)2)y(x)y(x)(a+x2+y(x)2)=0

Mathematica : cpu = 0.186808 (sec), leaf count = 71

DSolve[-(y[x]*(a + x^2 + y[x]^2)) + x*(-a + x^2 + y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
 
{{y(x)12(c1x4a+4x2+c12x2)},{y(x)12(4a+4x2+c12x2+c1x)}}

Maple : cpu = 0.096 (sec), leaf count = 112

dsolve(x*(y(x)^2+x^2-a)*diff(y(x),x)-y(x)*(y(x)^2+x^2+a) = 0,y(x))
 
11y(x)21x2+a=x2axc1+4ax2a+x22a2