4.61   ODE No. 1061

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\sqrt{x}+(1/4\frac{1}{\sqrt{x}}+x/4-9)y\left(x\right)-x{\mathrm{e}}^{-1/3x^{3/2}}=0}}$$

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

Mathematica: cpu = 0.076010 (sec), leaf count = 70 $$\left\{\{y(x)\to c_1{e}^{-\frac{1}{3}(\sqrt{x}+9)x}+\frac{1}{6}{c}_2{e}^{6x-\frac{1}{3}(\sqrt{x}+9)x}-\frac{1}{9}{e}^{3x-\frac{1}{3}(\sqrt{x}+9)x}x\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 38 $$\{y\left(x\right)={\mathrm{e}}^{-\frac{1}{3}{x}^{\frac{3}{2}}}\sinh \left(3x\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{-\frac{1}{3}{x}^{\frac{3}{2}}}\cosh \left(3x\right)\mathit{\_}\mathit{C}\mathit{1}-\frac{x}{9}{\mathrm{e}}^{-\frac{1}{3}{x}^{\frac{3}{2}}}\}$$