Internal problem ID [9050]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 715.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-\frac {-x^{2}+x +2+2 \sqrt {x^{2}-4 x +4 y}\, x^{3}}{2 \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 39
dsolve(diff(y(x),x) = 1/2*(-x^2+x+2+2*x^3*(x^2-4*x+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1} +\frac {2 x^{3}}{3}-x^{2}-2 \ln \left (x +1\right )+2 x -\sqrt {x^{2}-4 x +4 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 1.264 (sec). Leaf size: 50
DSolve[y'[x] == (1 + x/2 - x^2/2 + x^3*Sqrt[-4*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-x^2+\frac {1}{9} \left (2 x^3-3 x^2+6 x+6 \log \left (\frac {1}{x+1}\right )-6 c_1\right ){}^2+4 x\right ) \]