4.221   ODE No. 1221

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

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

Mathematica: cpu = 0.061508 (sec), leaf count = 40 $$\left\{\{y(x)\to c_1{J}_v(x)e^{{\int }_1^{x}f(K[1])dK[1]}+c_2{Y}_v(x)e^{{\int }_1^{x}f(K[1])dK[1]}\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 53 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{1}{2}\int \frac{-2xf\left(x\right)+1}{x}\mathrm{d}x}\sqrt{x}{\mathit{J}}_v\left(x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{1}{2}\int \frac{-2xf\left(x\right)+1}{x}\mathrm{d}x}\sqrt{x}{\mathit{Y}}_v\left(x\right)\}$$