ODE No. 294

$$x(-a+x^2+y(x{)}^2)y^{\prime }(x)-y(x)(a+x^2+y(x{)}^2)=0$$ ✓ Mathematica : cpu = 0.243601 (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]
 

$$\{\{y(x)\to \frac{1}{2}(c_{1}x-\sqrt{-4a+4x^2+c_1{}^2{x}^2})\},\{y(x)\to \frac{1}{2}(\sqrt{-4a+4x^2+c_1{}^2{x}^2}+c_{1}x)\}\}$$ ✓ Maple : cpu = 0.115 (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))
 

$$\frac{1}{\frac{1}{y{\left(x\right)}^2}-\frac{1}{-x^2+a}}=-\frac{\sqrt{x^2-a}x}{\sqrt{c_1+\frac{4a}{x^2-a}}}+\frac{x^2}{2}-\frac{a}{2}$$