4.439   ODE No. 1439

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=\frac{\left(\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{\varphi \left(x\right)-\varphi \left(a\right)}-\frac{(-n(n+1){(\varphi \left(x\right)-\varphi \left(a\right))}^2+\left(D^{\left(2\right)}\right)\left(\varphi \right)\left(a\right))y\left(x\right)}{\varphi \left(x\right)-\varphi \left(a\right)}=0}}$$

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

Mathematica: cpu = 0.765097 (sec), leaf count = 61 $$\text{DSolve}[y^{″}(x)=\frac{{\varphi }^{\prime }(x)y^{\prime }(x)}{\varphi (x)-\varphi (a)}-\frac{y(x)({\varphi }^{″}(a)-n(n+1)(\varphi (x)-\varphi (a){)}^2)}{\varphi (x)-\varphi (a)},y(x),x]$$

Maple: cpu = 0.671 (sec), leaf count = 69 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)-\frac{\left(\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)}{\varphi \left(x\right)-\varphi \left(a\right)}+\frac{(-n(n+1){(\varphi \left(x\right)-\varphi \left(a\right))}^2+\frac{{\mathrm{d}}^2}{\mathrm{d}{a}^2}\varphi \left(a\right))\mathit{\_}\mathit{Y}\left(x\right)}{\varphi \left(x\right)-\varphi \left(a\right)}\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$