2.1221   ODE No. 1221

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

$$y(x)(x^2(-f^{\prime }(x)+f(x{)}^2+1)-xf(x)-v^2)+(x-2x^{2}f(x))y^{\prime }(x)+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0587843 (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 = 0.026 (sec), leaf count = 53

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{1}{2}\int \frac{-2xf\left(x\right)+1}{x}\mathrm{d}x}\sqrt{x}{\mathit{J}}_v\left(x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{1}{2}\int \frac{-2xf\left(x\right)+1}{x}\mathrm{d}x}\sqrt{x}{\mathit{Y}}_v\left(x\right)\}$$