4.270   ODE No. 1270

$$\boxed{{\displaystyle (2x^2+6x+4)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(10x^2+21x+8)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(12x^2+17x+8)y\left(x\right)=0}}$$

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

Mathematica: cpu = 162.565643 (sec), leaf count = 57 $$\left\{\{y(x)\to c_2{e}^{-3x}(x+2{)}^4({\int }_1^x\frac{e^{K[1]}(K[1]+1{)}^{3/2}}{(K[1]+2{)}^5}dK[1])+c_1{e}^{-3x}(x+2{)}^4\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 54 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-2x}{(x+2)}^4\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(-1,-\frac{5}{2},4,-\frac{7}{4},\frac{7}{2},-1-x)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-2x}{(x+2)}^4{(1+x)}^{\frac{5}{2}}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(-1,\frac{5}{2},4,-\frac{7}{4},\frac{7}{2},-1-x)\}$$