5.68   ODE No. 1516

$$\boxed{{\displaystyle x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+(x+3)x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+5(x-6)x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(4x+30)y\left(x\right)=0}}$$

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

Mathematica: cpu = 434.677197 (sec), leaf count = 71 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {unicode {f818}^{(3)}(unicode {f817}) unicode {f817}^3+(unicode {f817}+3) unicode {f818}''(unicode {f817}) unicode {f817}^2+5 (unicode {f817}-6) unicode {f818}'(unicode {f817}) unicode {f817}+(4 unicode {f817}+30) unicode {f818}(unicode {f817})=0,unicode {f818}(1)=c\_1,unicode {f818}'(1)=c\_2,unicode {f818}''(1)=c\_3right }right )(x)right }right }}$$

Maple: cpu = 0.359 (sec), leaf count = 263 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(x^4-84x^3+2016x^2-20160x+75600)}{x^6}+\frac{\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-x}(x^8+28x^7+450x^6+5100x^5+42900x^4+267120x^3+1179360x^2+3326400x+4536000)}{x^6}+\frac{\mathit{\_}\mathit{C}\mathit{3}({\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)x^8+28{\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)x^7+450{\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)x^6+5100{\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)x^5+x^7+42900{\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)x^4+29x^6+60x^4\ln \left(x\right)+267120{\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)x^3+480x^5-5040x^3\ln \left(x\right)+1179360{\mathrm{e}}^{-x}{x}^2\mathit{E}\mathit{i}(1,-x)+5612x^4+120960x^2\ln \left(x\right)+3326400{\mathrm{e}}^{-x}x\mathit{E}\mathit{i}(1,-x)+40152x^3-1209600x\ln \left(x\right)+4536000{\mathrm{e}}^{-x}\mathit{E}\mathit{i}(1,-x)+654192x^2+4536000\ln \left(x\right)-2761920x+27367200)}{x^6}\}$$