2.1565   ODE No. 1565

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

$$(x(-{\rho }^2-{\sigma }^2+1)+16x^3)y^{\prime }(x)+y(x)({\rho }^2{\sigma }^2+8x^2)+(x^2(-{\rho }^2-{\sigma }^2+7)+4x^4)y^{″}(x)+x^4{y}^{(4)}(x)+6x^3{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 0.603238 (sec), leaf count = 242

$$\left\{\{y(x)\to c_1{x}^{-\rho }{}_2{F}_3(\frac{1}{2}-\frac{\rho }{2},1-\frac{\rho }{2};1-\rho ,-\frac{\rho }{2}-\frac{\sigma }{2}+1,-\frac{\rho }{2}+\frac{\sigma }{2}+1;-x^2)+c_3{x}^{-\sigma }{}_2{F}_3(\frac{1}{2}-\frac{\sigma }{2},1-\frac{\sigma }{2};1-\sigma ,-\frac{\rho }{2}-\frac{\sigma }{2}+1,\frac{\rho }{2}-\frac{\sigma }{2}+1;-x^2)+c_4{x}^{\sigma }{}_2{F}_3(\frac{\sigma }{2}+\frac{1}{2},\frac{\sigma }{2}+1;-\frac{\rho }{2}+\frac{\sigma }{2}+1,\frac{\rho }{2}+\frac{\sigma }{2}+1,\sigma +1;-x^2)+c_2{x}^{\rho }{}_2{F}_3(\frac{\rho }{2}+\frac{1}{2},\frac{\rho }{2}+1;\rho +1,\frac{\rho }{2}-\frac{\sigma }{2}+1,\frac{\rho }{2}+\frac{\sigma }{2}+1;-x^2)\}\right\}$$

✓ Maple : cpu = 0.463 (sec), leaf count = 71

$$\{y\left(x\right)=({\mathit{Y}}_{\frac{\rho }{2}-\frac{\sigma }{2}}\left(x\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathit{J}}_{\frac{\rho }{2}-\frac{\sigma }{2}}\left(x\right)\mathit{\_}\mathit{C}\mathit{1}){\mathit{J}}_{\frac{\sigma }{2}+\frac{\rho }{2}}\left(x\right)+{\mathit{Y}}_{\frac{\sigma }{2}+\frac{\rho }{2}}\left(x\right)({\mathit{Y}}_{\frac{\rho }{2}-\frac{\sigma }{2}}\left(x\right)\mathit{\_}\mathit{C}\mathit{4}+\mathit{\_}\mathit{C}\mathit{3}{\mathit{J}}_{\frac{\rho }{2}-\frac{\sigma }{2}}\left(x\right))\}$$