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 = 0.0259843 (sec), leaf count = 42

$$\left\{\{y(x)\to c_1{J}_v(x)\exp ({\int }_1^{x}f(K[1])dK[1])+c_2{Y}_v(x)\exp ({\int }_1^{x}f(K[1])dK[1])\}\right\}$$ ✓ Maple : cpu = 0.052 (sec), leaf count = 35

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