4.32   ODE No. 1032

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(1/2\frac{\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}g\left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)}-3/4\frac{{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}g\left(x\right)\right)}^2}{{\left(\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)\right)}^2}+\frac{(1/4-v^2){\left(\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)\right)}^2}{g\left(x\right)}+{\left(\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)\right)}^2)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.478061 (sec), leaf count = 71 $$\text{DSolve}[y(x)(\frac{(\frac{1}{4}-v^2)g^{\prime }(x{)}^2}{g(x)}+g^{\prime }(x{)}^2+\frac{g^3(x)}{2g^{\prime }(x)}-\frac{3g^{″}(x{)}^2}{4g^{\prime }(x{)}^2})+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.156 (sec), leaf count = 53 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{M}}_{\frac{i}{2}{v}^2-\frac{i}{8},\frac{1}{2}}\left(2ig\left(x\right)\right)\frac{1}{\sqrt{\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)}}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{W}}_{\frac{i}{2}{v}^2-\frac{i}{8},\frac{1}{2}}\left(2ig\left(x\right)\right)\frac{1}{\sqrt{\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)}}\}$$