2.1220   ODE No. 1220

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

$$y(x)(x^2(a+f^{\prime }(x)+f(x{)}^2)-(v-1)v)+2x^{2}f(x)y^{\prime }(x)+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0428519 (sec), leaf count = 98

$$\left\{\{y(x)\to c_1{J}_{\frac{1}{2}(2v-1)}\left(\sqrt{a}x\right)\exp ({\int }_1^x\frac{1-2f(K[1])K[1]}{2K[1]}dK[1])+c_2{Y}_{\frac{1}{2}(2v-1)}\left(\sqrt{a}x\right)\exp ({\int }_1^x\frac{1-2f(K[1])K[1]}{2K[1]}dK[1])\}\right\}$$ ✓ Maple : cpu = 0.078 (sec), leaf count = 40

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