8.161   ODE No. 1751

$$\boxed{{\displaystyle 4\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-3{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+(6{\left(y\left(x\right)\right)}^2-2\frac{\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right)y\left(x\right)}{f\left(x\right)})\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^4-2{\left(y\left(x\right)\right)}^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+g\left(x\right){\left(y\left(x\right)\right)}^2+f\left(x\right)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.742594 (sec), leaf count = 73 $$\text{DSolve}[y^{\prime }(x)(6y(x{)}^2-\frac{2y(x)f^{\prime }(x)}{f(x)})+f(x)y(x)+g(x)y(x{)}^2+4y(x)y^{″}(x)-2y(x{)}^2{y}^{\prime }(x)-3y^{\prime }(x{)}^2+y(x{)}^4=0,y(x),x]$$

Maple: cpu = 0.483 (sec), leaf count = 0 $$\text{could not solve}$$