2.1712   ODE No. 1712

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

$$-f(x)y(x)y^{\prime }(x)-g(x)y(x{)}^2-y^{\prime }(x{)}^2+y(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0587175 (sec), leaf count = 75

$$\left\{\{y(x)\to c_2\exp ({\int }_1^x(\exp ({\int }_1^{K[3]}f(K[1])dK[1])c_1+\exp ({\int }_1^{K[3]}f(K[1])dK[1]){\int }_1^{K[3]}\exp (-{\int }_1^{K[2]}f(K[1])dK[1])g(K[2])dK[2])dK[3])\}\right\}$$ ✓ Maple : cpu = 0.399 (sec), leaf count = 61

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{2}}{{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x}}{\mathrm{e}}^{\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x\int \frac{g\left(x\right)}{{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}}\mathrm{d}x}{\left({\mathrm{e}}^{\int \frac{\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}xg\left(x\right)}{{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}}\mathrm{d}x}\right)}^{-1}\}$$