6.8   ODE No. 1541

$$\boxed{{\displaystyle \mathit{d}\mathit{4}\mathit{y}\left(x\right)+(a{x}^2+b\lambda +c)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a{x}^2+\beta \lambda +\gamma )y\left(x\right)=0}}$$

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

Mathematica: cpu = 80.218186 (sec), leaf count = 73 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {left (a unicode {f817}^2+beta lambda +gamma right ) unicode {f818}(unicode {f817})+left (a unicode {f817}^2+c+b lambda right ) unicode {f818}''(unicode {f817})+unicode {f818}^{(4)}(unicode {f817})=0,unicode {f818}(0)=c\_1,unicode {f818}'(0)=c\_2,unicode {f818}''(0)=c\_3,unicode {f818}^{(3)}(0)=c\_4right }right )(x)right }right }}$$

Maple: cpu = 0.062 (sec), leaf count = 50 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{(a{x}^2+\beta \lambda +\gamma )\mathit{\_}\mathit{Y}\left(x\right)+(a{x}^2+b\lambda +c)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^4}{\mathrm{d}{x}^4}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$