4.343   ODE No. 1343

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-\frac{(x^{2}a(1-a)-b(x+b))y\left(x\right)}{x^4}=0}}$$

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

Mathematica: cpu = 0.665585 (sec), leaf count = 61 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {unicode {f818}''(unicode {f817}) unicode {f817}^4+left (-a^2 unicode {f817}^2+a unicode {f817}^2-b unicode {f817}-b^2right ) unicode {f818}(unicode {f817})=0,unicode {f818}(1)=c\_1,unicode {f818}'(1)=c\_2right }right )(x)right }right }}$$

Maple: cpu = 0.094 (sec), leaf count = 62 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}((2ax+b){\mathit{I}}_a\left(\frac{b}{x}\right)+{\mathit{I}}_{a+1}\left(\frac{b}{x}\right)b)+\mathit{\_}\mathit{C}\mathit{2}((2ax+b){\mathit{K}}_a\left(\frac{b}{x}\right)-{\mathit{K}}_{a+1}\left(\frac{b}{x}\right)b)\}$$