2.72   ODE No. 72

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{\prime }(x)-\text{R1}(x,\sqrt{\text{a0}+\text{a1}x+\text{a2}{x}^2+\text{a3}{x}^3+\text{a4}{x}^4})\text{R2}(y(x),\sqrt{\text{b0}+\text{b1}y(x)+\text{b2}y(x{)}^2+\text{b3}y(x{)}^3+\text{b4}y(x{)}^4})=0$$ ✓ Mathematica : cpu = 0.159416 (sec), leaf count = 89

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{\text{R2}(K[1],\sqrt{\text{b4}K[1{]}^4+\text{b3}K[1{]}^3+\text{b2}K[1{]}^2+\text{b1}K[1]+\text{b0}})}dK[1]\mathrm{\&}][{\int }_1^x\text{R1}(K[2],\sqrt{\text{a4}K[2{]}^4+\text{a3}K[2{]}^3+\text{a2}K[2{]}^2+\text{a1}K[2]+\text{a0}})dK[2]+c_1]\}\right\}$$ ✓ Maple : cpu = 0.012 (sec), leaf count = 64

$$\{\int \mathit{R}\mathit{1}(x,\sqrt{\mathit{a}\mathit{4}{x}^4+\mathit{a}\mathit{3}{x}^3+\mathit{a}\mathit{2}{x}^2+\mathit{a}\mathit{1}x+\mathit{a}\mathit{0}})\mathrm{d}x-{\int }^{y\left(x\right)}{\left(\mathit{R}\mathit{2}(\mathit{\_}\mathit{a},\sqrt{{\mathit{\_}\mathit{a}}^4\mathit{b}\mathit{4}+{\mathit{\_}\mathit{a}}^3\mathit{b}\mathit{3}+{\mathit{\_}\mathit{a}}^2\mathit{b}\mathit{2}+\mathit{\_}\mathit{a}\mathit{b}\mathit{1}+\mathit{b}\mathit{0}})\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$