Internal problem ID [9147]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 812.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-\sqrt {x^{3}-6 y}-\sqrt {x^{3}-6 y}\, x^{2}-x^{3} \sqrt {x^{3}-6 y}=\frac {x^{2}}{2}} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 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), singsol=all)
\[ c_{1} -\frac {3 x^{4}}{4}-x^{3}-3 x -\sqrt {x^{3}-6 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.618 (sec). Leaf size: 76
DSolve[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,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3 x^8}{32}-\frac {x^7}{4}-\frac {x^6}{6}-\frac {3 x^5}{4}+\left (-1+\frac {3 c_1}{4}\right ) x^4+\left (\frac {1}{6}+c_1\right ) x^3-\frac {3 x^2}{2}+3 c_1 x-\frac {3 c_1{}^2}{2} \]