2.1792   ODE No. 1792

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

$$a(y(x)-1)y(x)y^{″}(x)+y^{\prime }(x{)}^2(by(x)+c)+h(y(x))=0$$ ✓ Mathematica : cpu = 27.9638 (sec), leaf count = 222

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{K[2{]}^{-\frac{c}{a}}(1-K[2]{)}^{\frac{1}{2}(\frac{2b}{a}+\frac{2c}{a})}}{\sqrt{2{\int }_1^{K[2]}-\frac{h(K[1])\exp (-\frac{2(c\log (K[1])-(b+c)\log (1-K[1]))}{a})}{a(K[1]-1)K[1]}dK[1]+c_1}}dK[2]\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{K[3{]}^{-\frac{c}{a}}(1-K[3]{)}^{\frac{1}{2}(\frac{2b}{a}+\frac{2c}{a})}}{\sqrt{2{\int }_1^{K[3]}-\frac{h(K[1])\exp (-\frac{2(c\log (K[1])-(b+c)\log (1-K[1]))}{a})}{a(K[1]-1)K[1]}dK[1]+c_1}}dK[3]\mathrm{\&}][c_2+x]\}\}$$

✓ Maple : cpu = 1.03 (sec), leaf count = 194

$$\{{\int }^{y\left(x\right)}a\frac{1}{\sqrt{a(\mathit{\_}\mathit{C}\mathit{1}a-2\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}{\left({(\mathit{\_}\mathit{b}-1)}^{\frac{b}{a}}\right)}^2{\left({(\mathit{\_}\mathit{b}-1)}^{\frac{c}{a}}\right)}^2{\left({\mathit{\_}\mathit{b}}^{\frac{c}{a}}\right)}^{-2}\mathrm{d}\mathit{\_}\mathit{b})}}{\left({\mathit{\_}\mathit{b}}^{\frac{c}{a}}\right)}^{-1}{\left({(\mathit{\_}\mathit{b}-1)}^{\frac{-b-c}{a}}\right)}^{-1}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-a\frac{1}{\sqrt{a(\mathit{\_}\mathit{C}\mathit{1}a-2\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}{\left({(\mathit{\_}\mathit{b}-1)}^{\frac{b}{a}}\right)}^2{\left({(\mathit{\_}\mathit{b}-1)}^{\frac{c}{a}}\right)}^2{\left({\mathit{\_}\mathit{b}}^{\frac{c}{a}}\right)}^{-2}\mathrm{d}\mathit{\_}\mathit{b})}}{\left({\mathit{\_}\mathit{b}}^{\frac{c}{a}}\right)}^{-1}{\left({(\mathit{\_}\mathit{b}-1)}^{\frac{-b-c}{a}}\right)}^{-1}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$