2.1061   ODE No. 1061

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

$$-e^{-\frac{x^{3/2}}{3}}x+y^{″}(x)+\sqrt{x}{y}^{\prime }(x)+(\frac{x}{4}+\frac{1}{4\sqrt{x}}-9)y(x)=0$$ ✓ Mathematica : cpu = 0.0763434 (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 = 0.08 (sec), leaf count = 38

$$\{y\left(x\right)={\mathrm{e}}^{-\frac{1}{3}{x}^{\frac{3}{2}}}\sinh \left(3x\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{-\frac{1}{3}{x}^{\frac{3}{2}}}\cosh \left(3x\right)\mathit{\_}\mathit{C}\mathit{1}-\frac{x}{9}{\mathrm{e}}^{-\frac{1}{3}{x}^{\frac{3}{2}}}\}$$