2.1720   ODE No. 1720

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

$$a{y}^{\prime }(x{)}^2+by(x{)}^2{y}^{\prime }(x)+cy(x{)}^4+y(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 88.0957 (sec), leaf count = 105

$$\text{Solve}[{\int }_1^{y(x)}\frac{1}{K[2{]}^2\text{InverseFunction}\left[\frac{\log (c+\mathrm{\#}\text{1}(b+(a+2)\mathrm{\#}\text{1}))-\frac{2b{\tan }^{-1}\left(\frac{b+2(a+2)\mathrm{\#}\text{1}}{\sqrt{4(a+2)c-b^2}}\right)}{\sqrt{4(a+2)c-b^2}}}{2(a+2)}\mathrm{\&}\right][c_1-\log (K[2])]}dK[2]=x-c_2,y(x)]$$ ✓ Maple : cpu = 1.628 (sec), leaf count = 173

$$\{-c_2-x+{\int }_{}^{y\left(x\right)}\frac{2a+4}{-{\mathit{\text{\_a}}}^{2}b+\sqrt{-{\mathit{\text{\_a}}}^4{b}^2+(4a+8){\mathit{\text{\_a}}}^{4}c}\tan \left(\mathrm{RootOf}(2\mathit{\text{\_Z}}{\mathit{\text{\_a}}}^{2}b-2\sqrt{4{\mathit{\text{\_a}}}^{4}ac-{\mathit{\text{\_a}}}^4{b}^2+8c{\mathit{\text{\_a}}}^4}a\ln \left(\mathit{\text{\_a}}\right)+c_1\sqrt{4{\mathit{\text{\_a}}}^{4}ac-{\mathit{\text{\_a}}}^4{b}^2+8c{\mathit{\text{\_a}}}^4}-\sqrt{4{\mathit{\text{\_a}}}^{4}ac-{\mathit{\text{\_a}}}^4{b}^2+8c{\mathit{\text{\_a}}}^4}\ln \left(\frac{({\tan }^2\left(\mathit{\text{\_Z}}\right)+1)(4ac-b^2+8c){\mathit{\text{\_a}}}^4}{4a+8}\right))\right)}d\mathit{\text{\_a}}=0\}$$