4.85   ODE No. 1085

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

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

Mathematica: cpu = 0.922617 (sec), leaf count = 118 $$\text{DSolve}[-y^{\prime }(x)(\frac{(2v-1)g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)}+\frac{2h^{\prime }(x)}{h(x)})+y(x)(g^{\prime }(x{)}^2+\frac{h^{\prime }(x)(\frac{(2v-1)g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)}+\frac{2h^{\prime }(x)}{h(x)})}{h(x)}-\frac{h^{″}(x)}{h(x)})+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.062 (sec), leaf count = 29 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_v\left(g\left(x\right)\right)h\left(x\right){\left(g\left(x\right)\right)}^v+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_v\left(g\left(x\right)\right)h\left(x\right){\left(g\left(x\right)\right)}^v\}$$