ODE No. 819

$$y^{\prime }(x)=x^2\sqrt{x^2+3y(x)}+\sqrt{x^2+3y(x)}+x^3\sqrt{x^2+3y(x)}-\frac{2x}{3}$$ ✓ Mathematica : cpu = 0.307955 (sec), leaf count = 65

DSolve[Derivative[1][y][x] == (-2*x)/3 + Sqrt[x^2 + 3*y[x]] + x^2*Sqrt[x^2 + 3*y[x]] + x^3*Sqrt[x^2 + 3*y[x]],y[x],x]
 

$$\left\{\{y(x)\to \frac{1}{192}(9x^8+24x^7+16x^6+72x^5+96x^4-72c_1{x}^4-96c_1{x}^3+80x^2-288c_{1}x+144c_1{}^2)\}\right\}$$ ✓ Maple : cpu = 0.294 (sec), leaf count = 30

dsolve(diff(y(x),x) = -2/3*x+(x^2+3*y(x))^(1/2)+x^2*(x^2+3*y(x))^(1/2)+x^3*(x^2+3*y(x))^(1/2),y(x))
 

$$c_1+\frac{3x^4}{8}+\frac{x^3}{2}+\frac{3x}{2}-\sqrt{x^2+3y\left(x\right)}=0$$