10.30   ODE No. 1885

$$\boxed{{\displaystyle \{t\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+2\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+tx\left(t\right)=0,t\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-t\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)-2y\left(t\right)=0\}}}$$

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

Mathematica: cpu = 0.022503 (sec), leaf count = 47 $$\text{DSolve}[\{t{x}^{\prime }(t)-t{y}^{\prime }(t)-2y(t)=0,t{x}^{″}(t)+2x^{\prime }(t)+tx(t)=0\},\{x(t),y(t)\},t]$$

Maple: cpu = 0.078 (sec), leaf count = 47 $$\left\{\{x\left(t\right)=\frac{\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{3}\cos \left(t\right)}{t},y\left(t\right)=\frac{\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{2}t+\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{3}t-2\mathit{\_}\mathit{C}\mathit{3}\sin \left(t\right)+2\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{1}}{t^2}\}\right\}$$