2.819   ODE No. 819

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

$$y^{\prime }(x)=x^3\sqrt{x^2+3y(x)}+x^2\sqrt{x^2+3y(x)}+\sqrt{x^2+3y(x)}-\frac{2x}{3}$$ ✓ Mathematica : cpu = 0.279622 (sec), leaf count = 65

$$\left\{\{y(x)\to \frac{1}{192}(9x^8+24x^7+16x^6+72x^5+96x^4+80x^2-72c_1{x}^4-96c_1{x}^3-288c_{1}x+144c_1{}^2)\}\right\}$$ ✓ Maple : cpu = 0.468 (sec), leaf count = 30

$$\{\mathit{\_}\mathit{C}\mathit{1}+\frac{3x^4}{8}+\frac{x^3}{2}+\frac{3x}{2}-\sqrt{x^2+3y\left(x\right)}=0\}$$