11.13   ODE No. 1925

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

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

Mathematica: cpu = 8.399567 (sec), leaf count = 55 $$\text{DSolve}[\{a{y}^{\prime }(t)+t{x}^{\prime }(t)-x(t)+y^{\prime }(t{)}^2=0,x^{\prime }(t)y^{\prime }(t)+t{y}^{\prime }(t)-y(t)=0\},\{x(t),y(t)\},t]$$

Maple: cpu = 0.219 (sec), leaf count = 226 $$\{[\{x\left(t\right)=-\frac{t^2}{3}\},\{y\left(t\right)=-\frac{t^3}{27a}\}],[\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}t+\mathit{\_}\mathit{C}\mathit{2}\},\{y\left(t\right)=\frac{-{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^3-2{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^{2}t-\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)t^2+x\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+tx\left(t\right)}{a}\}],[\{x\left(t\right)=-\frac{5{\mathit{\_}\mathit{C}\mathit{1}}^2{t}^2+2\mathit{\_}\mathit{C}\mathit{1}t(-\mathit{\_}\mathit{C}\mathit{1}t+\sqrt{3})-3}{12{\mathit{\_}\mathit{C}\mathit{1}}^2},x\left(t\right)=-\frac{5{\mathit{\_}\mathit{C}\mathit{1}}^2{t}^2-2\mathit{\_}\mathit{C}\mathit{1}t(\mathit{\_}\mathit{C}\mathit{1}t+\sqrt{3})-3}{12{\mathit{\_}\mathit{C}\mathit{1}}^2},x\left(t\right)=-\frac{5t^2}{12}+\frac{t(t-\sqrt{3}\mathit{\_}\mathit{C}\mathit{1})}{6}+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{4},x\left(t\right)=-\frac{5t^2}{12}+\frac{t(t+\sqrt{3}\mathit{\_}\mathit{C}\mathit{1})}{6}+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{4}\},\{y\left(t\right)=-\frac{-2\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)t^2-2t^3-6x\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-7tx\left(t\right)}{9a}\}]\}$$