4.154   ODE No. 1154

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a{x}^2+bx+c)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.020002 (sec), leaf count = 88 $$\left\{\{y(x)\to c_1{M}_{-\frac{ib}{2\sqrt{a}},-\frac{1}{2}i\sqrt{4c-1}}\left(2i\sqrt{a}x\right)+c_2{W}_{-\frac{ib}{2\sqrt{a}},-\frac{1}{2}i\sqrt{4c-1}}\left(2i\sqrt{a}x\right)\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 57 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{M}}_{-\frac{i}{2}b\frac{1}{\sqrt{a}},\frac{1}{2}\sqrt{1-4c}}\left(2i\sqrt{a}x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{W}}_{-\frac{i}{2}b\frac{1}{\sqrt{a}},\frac{1}{2}\sqrt{1-4c}}\left(2i\sqrt{a}x\right)\}$$