Internal problem ID [8392]
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)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}}{2}-\sqrt {x^{3}-6 y}-x^{2} \sqrt {x^{3}-6 y}-x^{3} \sqrt {x^{3}-6 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.37 (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)
\[ c_{1}-\frac {3 x^{4}}{4}-x^{3}-3 x -\sqrt {x^{3}-6 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.607 (sec). Leaf size: 63
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]
\begin{align*} y(x)\to -\frac {1}{96} \left (x \left (x (3 x+4) \left ((3 x+4) x^2+24\right )-16\right )+144\right ) x^2+\frac {1}{4} c_1 \left ((3 x+4) x^2+12\right ) x-\frac {3 c_1{}^2}{2} \\ \end{align*}