Internal problem ID [9047]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 712.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-\frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}\, x^{3}}{2 \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 38
dsolve(diff(y(x),x) = 1/2*(x^2+2*x+1+2*x^3*(x^2+2*x+1-4*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1} -\frac {2 x^{3}}{3}+x^{2}-2 x +2 \ln \left (x +1\right )-\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 1.212 (sec). Leaf size: 49
DSolve[y'[x] == (1/2 + x + x^2/2 + x^3*Sqrt[1 + 2*x + x^2 - 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (x^2-\frac {1}{9} \left (2 x^3-3 x^2+6 x+6 \log \left (\frac {1}{x+1}\right )-6 c_1\right ){}^2+2 x+1\right ) \]