Internal problem ID [8399]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 819.
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 {2 x}{3}-\sqrt {x^{2}+3 y}-x^{2} \sqrt {x^{2}+3 y}-x^{3} \sqrt {x^{2}+3 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.422 (sec). Leaf size: 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), singsol=all)
\[ c_{1}+\frac {3 x^{4}}{8}+\frac {x^{3}}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.446 (sec). Leaf size: 45
DSolve[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,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{192} \left (3 x^4+4 x^3+4 x-12 c_1\right ) \left (3 x^4+4 x^3+20 x-12 c_1\right ) \\ \end{align*}