8.224   ODE No. 1814

$$\boxed{{\displaystyle h\left(y\left(x\right)\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a\text{D}\left(h\right)\left(y\left(x\right)\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+j\left(y\left(x\right)\right)=0}}$$

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

Mathematica: cpu = 13.253683 (sec), leaf count = 116 $$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{e^{aK[2]}}{\sqrt{2{\int }_1^{K[2]}-\frac{e^{2aK[1]}j(K[1])}{h(K[1])}dK[1]+c_1}}dK[2]\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{e^{aK[3]}}{\sqrt{2{\int }_1^{K[3]}-\frac{e^{2aK[1]}j(K[1])}{h(K[1])}dK[1]+c_1}}dK[3]\mathrm{\&}][c_2+x]\}\}$$

Maple: cpu = 0.125 (sec), leaf count = 90 $$\{{\int }^{y\left(x\right)}\frac{1}{{\left(h\left(\mathit{\_}\mathit{b}\right)\right)}^{-a}}\frac{1}{\sqrt{-2\int \frac{{\left({\left(h\left(\mathit{\_}\mathit{b}\right)\right)}^a\right)}^{2}j\left(\mathit{\_}\mathit{b}\right)}{h\left(\mathit{\_}\mathit{b}\right)}\mathrm{d}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{{\left(h\left(\mathit{\_}\mathit{b}\right)\right)}^{-a}}\frac{1}{\sqrt{-2\int \frac{{\left({\left(h\left(\mathit{\_}\mathit{b}\right)\right)}^a\right)}^{2}j\left(\mathit{\_}\mathit{b}\right)}{h\left(\mathit{\_}\mathit{b}\right)}\mathrm{d}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$