2.1568   ODE No. 1568

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

$$ay(x)+x^4{y}^{(4)}(x)+8x^3{y}^{(3)}(x)+12x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0129222 (sec), leaf count = 122

$$\left\{\{y(x)\to c_1{x}^{\frac{1}{2}(-\sqrt{5-4\sqrt{1-a}}-1)}+c_2{x}^{\frac{1}{2}(\sqrt{5-4\sqrt{1-a}}-1)}+c_3{x}^{\frac{1}{2}(-\sqrt{4\sqrt{1-a}+5}-1)}+c_4{x}^{\frac{1}{2}(\sqrt{4\sqrt{1-a}+5}-1)}\}\right\}$$

✓ Maple : cpu = 0.027 (sec), leaf count = 89

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{1}{2}-\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{1}{2}+\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{3}{x}^{-\frac{1}{2}-\frac{1}{2}\sqrt{5+4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{4}{x}^{-\frac{1}{2}+\frac{1}{2}\sqrt{5+4\sqrt{1-a}}}\}$$