Internal problem ID [8242]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 662.
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}{2}-\frac {1}{2}-x^{2} \sqrt {x^{2}+2 x +1-4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.282 (sec). Leaf size: 26
dsolve(diff(y(x),x) = 1/2*x+1/2+x^2*(x^2+2*x+1-4*y(x))^(1/2),y(x), singsol=all)
\[ c_{1}-\frac {2 x^{3}}{3}-\sqrt {x^{2}-4 y \relax (x )+2 x +1} = 0 \]
✓ Solution by Mathematica
Time used: 0.746 (sec). Leaf size: 37
DSolve[y'[x] == 1/2 + x/2 + x^2*Sqrt[1 + 2*x + x^2 - 4*y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{36} \left (-4 x^6+24 c_1 x^3+9 x^2+18 x+9-36 c_1{}^2\right ) \\ \end{align*}