2.1551   ODE No. 1551

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

$$-2({\nu }^2{x}^2+6)y^{″}(x)+{\nu }^2({\nu }^2{x}^2+4)y(x)+x^2{y}^{(4)}(x)=0$$ ✓ Mathematica : cpu = 0.291807 (sec), leaf count = 110

$$\left\{\{y(x)\to \frac{c_3(1-x)e^{-\nu x}({\nu }^2{x}^2+{\nu }^{2}x+{\nu }^2+6\nu x+6\nu +15)}{x}+\frac{c_4(1-x)e^{\nu x}({\nu }^2{x}^2+{\nu }^{2}x+{\nu }^2-6\nu x-6\nu +15)}{x}+\frac{c_1{e}^{-\nu x}}{x}+\frac{c_2{e}^{\nu x}}{x}\}\right\}$$ ✓ Maple : cpu = 0.212 (sec), leaf count = 62

$$\{y\left(x\right)=\frac{(\mathit{\_}\mathit{C}\mathit{4}{\nu }^2{x}^3+6\mathit{\_}\mathit{C}\mathit{4}\nu x^2+15\mathit{\_}\mathit{C}\mathit{4}x+\mathit{\_}\mathit{C}\mathit{2}){\mathrm{e}}^{-\nu x}+{\mathrm{e}}^{\nu x}(\mathit{\_}\mathit{C}\mathit{3}{\nu }^2{x}^3-6\mathit{\_}\mathit{C}\mathit{3}\nu x^2+15\mathit{\_}\mathit{C}\mathit{3}x+\mathit{\_}\mathit{C}\mathit{1})}{x}\}$$