2.812   ODE No. 812

\[ y'(x)=x^3 \sqrt {x^3-6 y(x)}+\sqrt {x^3-6 y(x)}+\frac {x^2}{2}+x^2 \sqrt {x^3-6 y(x)} \]

✓ Mathematica : cpu = 0.288781 (sec), leaf count = 70

DSolve[Derivative[1][y][x] == x^2/2 + Sqrt[x^3 - 6*y[x]] + x^2*Sqrt[x^3 - 6*y[x]] + x^3*Sqrt[x^3 - 6*y[x]],y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{96} \left (-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4+72 c_1 x^4+16 x^3+96 c_1 x^3-144 x^2+288 c_1 x-144 c_1{}^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.306 (sec), leaf count = 30

dsolve(diff(y(x),x) = 1/2*x^2+(x^3-6*y(x))^(1/2)+x^2*(x^3-6*y(x))^(1/2)+x^3*(x^3-6*y(x))^(1/2),y(x))
 

\[c_{1} -\frac {3 x^{4}}{4}-x^{3}-3 x -\sqrt {x^{3}-6 y \left (x \right )} = 0\]