ODE No. 906

$$y^{\prime }(x)=\frac{x(x^2+y(x{)}^2+1)}{x^6+3x^{4}y(x{)}^2+3x^{2}y(x{)}^4-x^{2}y(x)+y(x{)}^6-y(x{)}^3-y(x)}$$ ✓ Mathematica : cpu = 0.137126 (sec), leaf count = 326

DSolve[Derivative[1][y][x] == (x*(1 + x^2 + y[x]^2))/(x^6 - y[x] - x^2*y[x] + 3*x^4*y[x]^2 - y[x]^3 + 3*x^2*y[x]^4 + y[x]^6),y[x],x]
 

$$\{\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},1]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},2]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},3]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},4]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},5]\}\}$$ ✓ Maple : cpu = 0.284 (sec), leaf count = 37

dsolve(diff(y(x),x) = x*(x^2+y(x)^2+1)/(-y(x)^3-x^2*y(x)-y(x)+y(x)^6+3*x^2*y(x)^4+3*x^4*y(x)^2+x^6),y(x))
 

$$-\frac{1}{4{(y{\left(x\right)}^2+x^2)}^2}-\frac{1}{2y{\left(x\right)}^2+2x^2}-y\left(x\right)+c_1=0$$