5.26   ODE No. 1474

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

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

Mathematica: cpu = 0.015002 (sec), leaf count = 55 $$\text{DSolve}[y^{\prime }(x)(f^{\prime }(x)+2f(x{)}^2+4g(x))+y(x)(4f(x)g(x)+2g^{\prime }(x))+3f(x)y^{″}(x)+y^{(3)}(x)=0,y(x),x]$$

Maple: cpu = 0.110 (sec), leaf count = 30 $$\{y\left(x\right)={\left(\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+f\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+g\left(x\right)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\right)}^2\}$$