ODE No. 918

$$y^{\prime }(x)=\frac{2y(x{)}^8}{128x^{3}y(x{)}^6+32x^{2}y(x{)}^6+96x^{2}y(x{)}^4+2y(x{)}^6+y(x{)}^5+16xy(x{)}^4+24xy(x{)}^2+2y(x{)}^2+2}$$ ✓ Mathematica : cpu = 0.489549 (sec), leaf count = 720

DSolve[Derivative[1][y][x] == (2*y[x]^8)/(2 + 2*y[x]^2 + 24*x*y[x]^2 + 16*x*y[x]^4 + 96*x^2*y[x]^4 + y[x]^5 + 2*y[x]^6 + 32*x^2*y[x]^6 + 128*x^3*y[x]^6),y[x],x]
 

$$\text{Solve}[{\int }_1^{y(x)}(\text{RootSum}[64{\mathrm{\#}\text{1}}^{3}K[1{]}^6+16{\mathrm{\#}\text{1}}^{2}K[1{]}^6+K[1{]}^6+48{\mathrm{\#}\text{1}}^{2}K[1{]}^4+8\mathrm{\#}\text{1}K[1{]}^4+12\mathrm{\#}\text{1}K[1{]}^2+K[1{]}^2+1\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{48{\mathrm{\#}\text{1}}^{2}K[1{]}^4+8\mathrm{\#}\text{1}K[1{]}^4+24\mathrm{\#}\text{1}K[1{]}^2+2K[1{]}^2+3}\mathrm{\&}]K[1{]}^3+\frac{K[1{]}^3}{2(64x^{3}K[1{]}^6+16x^{2}K[1{]}^6+K[1{]}^6+48x^{2}K[1{]}^4+8xK[1{]}^4+12xK[1{]}^2+K[1{]}^2+1)}-\frac{\text{RootSum}[64{\mathrm{\#}\text{1}}^{3}K[1{]}^6+16{\mathrm{\#}\text{1}}^{2}K[1{]}^6+K[1{]}^6+48{\mathrm{\#}\text{1}}^{2}K[1{]}^4+8\mathrm{\#}\text{1}K[1{]}^4+12\mathrm{\#}\text{1}K[1{]}^2+K[1{]}^2+1\mathrm{\&},\frac{128x\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^6+320\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^6-24x\log (x-\mathrm{\#}\text{1})K[1{]}^6+2\log (x-\mathrm{\#}\text{1})K[1{]}^6-288x\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^6+24\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^6+32\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^4+16{\mathrm{\#}\text{1}}^{2}K[1{]}^4-72x\log (x-\mathrm{\#}\text{1})K[1{]}^4+64x\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^4+88\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^4-36\mathrm{\#}\text{1}K[1{]}^4-3K[1{]}^4+8x\log (x-\mathrm{\#}\text{1})K[1{]}^2+2\log (x-\mathrm{\#}\text{1})K[1{]}^2+16\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^2+8\mathrm{\#}\text{1}K[1{]}^2-9K[1{]}^2+2\log (x-\mathrm{\#}\text{1})+1}{64x{\mathrm{\#}\text{1}}^{2}K[1{]}^6+160{\mathrm{\#}\text{1}}^{2}K[1{]}^6+112xK[1{]}^6-144x\mathrm{\#}\text{1}K[1{]}^6-112\mathrm{\#}\text{1}K[1{]}^6+K[1{]}^6+16{\mathrm{\#}\text{1}}^{2}K[1{]}^4-36xK[1{]}^4+32x\mathrm{\#}\text{1}K[1{]}^4+44\mathrm{\#}\text{1}K[1{]}^4+4xK[1{]}^2+8\mathrm{\#}\text{1}K[1{]}^2+K[1{]}^2+1}\mathrm{\&}]}{2K[1]}+\frac{1}{K[1{]}^2})dK[1]-\frac{1}{4}y(x{)}^4\text{RootSum}[64{\mathrm{\#}\text{1}}^{3}y(x{)}^6+16{\mathrm{\#}\text{1}}^{2}y(x{)}^6+48{\mathrm{\#}\text{1}}^{2}y(x{)}^4+8\mathrm{\#}\text{1}y(x{)}^4+12\mathrm{\#}\text{1}y(x{)}^2+y(x{)}^6+y(x{)}^2+1\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{48{\mathrm{\#}\text{1}}^{2}y(x{)}^4+8\mathrm{\#}\text{1}y(x{)}^4+24\mathrm{\#}\text{1}y(x{)}^2+2y(x{)}^2+3}\mathrm{\&}]=c_1,y(x)]$$ ✓ Maple : cpu = 1.171 (sec), leaf count = 41

dsolve(diff(y(x),x) = 2*y(x)^8/(y(x)^5+2*y(x)^6+2*y(x)^2+16*x*y(x)^4+32*y(x)^6*x^2+2+24*x*y(x)^2+96*x^2*y(x)^4+128*x^3*y(x)^6),y(x))
 

$$x-\mathrm{RootOf}(\left({\int }_{}^{\mathit{\text{\_Z}}}\frac{1}{64{\mathit{\text{\_a}}}^3+16{\mathit{\text{\_a}}}^2+1}d\mathit{\text{\_a}}\right)y\left(x\right)+c_{1}y\left(x\right)+1)+\frac{1}{4y{\left(x\right)}^2}=0$$