8.122   ODE No. 1712

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-f\left(x\right)y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-g\left(x\right){\left(y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 10.804372 (sec), leaf count = 70 $$\left\{\{y(x)\to c_2\exp ({\int }_1^x(c_1{e}^{{\int }_1^{K[3]}f(K[1])dK[1]}+e^{{\int }_1^{K[3]}f(K[1])dK[1]}{\int }_1^{K[3]}g(K[2])e^{-{\int }_1^{K[2]}f(K[1])dK[1]}dK[2])dK[3])\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 61 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{2}}{{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x}}{\mathrm{e}}^{\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x\int \frac{g\left(x\right)}{{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}}\mathrm{d}x}{\left({\mathrm{e}}^{\int \frac{\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}xg\left(x\right)}{{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}}\mathrm{d}x}\right)}^{-1}\}$$