3.33   ODE No. 33

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

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

Mathematica: cpu = 26.354347 (sec), leaf count = 157 $$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{(f(x)K[2]+g(x){)}^2}-{\int }_1^x(\frac{2(K[2{]}^{2}f(K[1])f^{\prime }(K[1])-g(K[1])g^{\prime }(K[1]))}{g(K[1])(K[2]f(K[1])+g(K[1]){)}^3}-\frac{2K[2]f^{\prime }(K[1])}{g(K[1])(K[2]f(K[1])+g(K[1]){)}^2})dK[1])dK[2]+{\int }_1^x-\frac{y(x{)}^{2}f(K[1])f^{\prime }(K[1])-g(K[1])g^{\prime }(K[1])}{f(K[1])g(K[1])(y(x)f(K[1])+g(K[1]){)}^2}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.343 (sec), leaf count = 57 $$\{y\left(x\right)=-\frac{1}{{\left(f\left(x\right)\right)}^2}(g\left(x\right)f\left(x\right)\int \frac{\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)}{g\left(x\right){\left(f\left(x\right)\right)}^2}\mathrm{d}x+g\left(x\right)f\left(x\right)\mathit{\_}\mathit{C}\mathit{1}+1){(\mathit{\_}\mathit{C}\mathit{1}+\int \frac{\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)}{g\left(x\right){\left(f\left(x\right)\right)}^2}\mathrm{d}x)}^{-1}\}$$

Sage: cpu = 0.1 (sec), leaf count = 0 $$[\left[[y\left(x\right)=0,-\frac{uD[0]\left(f\right){\left(x\right)}^{2}D[0]\left(g\right)\left(x\right)}{f\left(x\right)g{\left(x\right)}^2}=0]\right],\mathtt{\text{riccati}}]$$