Internal problem ID [9013]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 678.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-\frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 \left (1+x \right )}=0} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 37
dsolve(diff(y(x),x) = 1/2*x^2*(x+1+2*x*(x^3-6*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1} -x^{3}+\frac {3 x^{2}}{2}-3 x +3 \ln \left (x +1\right )-\frac {1}{2}-\sqrt {x^{3}-6 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 4.061 (sec). Leaf size: 99
DSolve[y'[x] == (x^2*(1 + x + 2*x*Sqrt[x^3 - 6*y[x]]))/(2*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} \left (-4 x^6+12 x^5-33 x^4+4 (-1+6 c_1) x^3-6 (-5+6 c_1) x^2+12 \left (2 x^3-3 x^2+6 x+11-6 c_1\right ) \log (x+1)-36 \log ^2(x+1)+12 (-11+6 c_1) x-(11-6 c_1){}^2\right ) \]