Internal problem ID [8279]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 699.
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 \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.396 (sec). Leaf size: 36
dsolve(diff(y(x),x) = 1/3*x*(-2*x-2+3*x^2*(x^2+3*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1}+\frac {x^{3}}{2}-\frac {3 x^{2}}{4}-\frac {3 \ln \left (x +1\right )}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.686 (sec). Leaf size: 86
DSolve[y'[x] == (x*(-2 - 2*x + 3*x^2*Sqrt[x^2 + 3*y[x]]))/(3*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{6} \left (2 x^3-4 \sqrt {x^2+3 y(x)}-6 \log \left ((x+1) \left (\sqrt {x^2+3 y(x)}-x\right )\right )-6 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+3 y(x)}}\right )-3 x^2+6 x\right )+\frac {1}{2} \log (y(x))=c_1,y(x)\right ] \]