ODE No. 70

$$y^{\prime }(x)-\sqrt{\frac{\text{a0}+\text{a1}x+\text{a2}{x}^2+\text{a3}{x}^3+\text{a4}{x}^4}{\text{b0}+\text{b1}y(x)+\text{b2}y(x{)}^2+\text{b3}y(x{)}^3+\text{b4}y(x{)}^4}}=0$$ ✓ Mathematica : cpu = 12.7936 (sec), leaf count = 81

DSolve[-Sqrt[(a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4)/(b0 + b1*y[x] + b2*y[x]^2 + b3*y[x]^3 + b4*y[x]^4)] + Derivative[1][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\sqrt{\text{b4}K[1{]}^4+\text{b3}K[1{]}^3+\text{b2}K[1{]}^2+\text{b1}K[1]+\text{b0}}dK[1]\mathrm{\&}][{\int }_1^x\sqrt{\text{a4}K[2{]}^4+\text{a3}K[2{]}^3+\text{a2}K[2{]}^2+\text{a1}K[2]+\text{a0}}dK[2]+c_1]\}\right\}$$ ✓ Maple : cpu = 0.174 (sec), leaf count = 113

dsolve(diff(y(x),x)-((a4*x^4+a3*x^3+a2*x^2+a1*x+a0)/(b4*y(x)^4+b3*y(x)^3+b2*y(x)^2+b1*y(x)+b0))^(1/2) = 0,y(x))
 

$${\int }_{}^{y\left(x\right)}\sqrt{{\mathit{\text{\_a}}}^4\mathit{b}\mathit{4}+{\mathit{\text{\_a}}}^3\mathit{b}\mathit{3}+{\mathit{\text{\_a}}}^2\mathit{b}\mathit{2}+\mathit{\text{\_a}}\mathit{b}\mathit{1}+\mathit{b}\mathit{0}}d\mathit{\text{\_a}}+{\int }_{}^x-\sqrt{\frac{{\mathit{\text{\_a}}}^4\mathit{a}\mathit{4}+{\mathit{\text{\_a}}}^3\mathit{a}\mathit{3}+{\mathit{\text{\_a}}}^2\mathit{a}\mathit{2}+\mathit{\text{\_a}}\mathit{a}\mathit{1}+\mathit{a}\mathit{0}}{\mathit{b}\mathit{4}y{\left(x\right)}^4+\mathit{b}\mathit{3}y{\left(x\right)}^3+\mathit{b}\mathit{2}y{\left(x\right)}^2+\mathit{b}\mathit{1}y\left(x\right)+\mathit{b}\mathit{0}}}\sqrt{\mathit{b}\mathit{4}y{\left(x\right)}^4+\mathit{b}\mathit{3}y{\left(x\right)}^3+\mathit{b}\mathit{2}y{\left(x\right)}^2+\mathit{b}\mathit{1}y\left(x\right)+\mathit{b}\mathit{0}}d\mathit{\text{\_a}}+c_1=0$$