5.83   ODE No. 1531

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

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

Mathematica: cpu = 0.034004 (sec), leaf count = 76 $$\text{DSolve}[A(x)(f(x)y^{″}(x)+g(x)y^{\prime }(x)+h(x)y(x))+f^{\prime }(x)y^{″}(x)+f(x)y^{(3)}(x)+g^{\prime }(x)y^{\prime }(x)+g(x)y^{″}(x)+y(x)h^{\prime }(x)+h(x)y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 0.125 (sec), leaf count = 70 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{f\left(x\right)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}\mathit{\_}\mathit{Y}\left(x\right)+(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)+g\left(x\right)+A\left(x\right)f\left(x\right))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+(\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)+h\left(x\right)+A\left(x\right)g\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(\frac{\mathrm{d}}{\mathrm{d}x}h\left(x\right)+A\left(x\right)h\left(x\right))\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$