Internal problem ID [8233]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 653.
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}-1-x \sqrt {x^{2}-4 x +4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.263 (sec). Leaf size: 24
dsolve(diff(y(x),x) = -1/2*x+1+x*(x^2-4*x+4*y(x))^(1/2),y(x), singsol=all)
\[ c_{1}+x^{2}+\frac {1}{4}-\sqrt {x^{2}+4 y \relax (x )-4 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.528 (sec). Leaf size: 31
DSolve[y'[x] == 1 - x/2 + x*Sqrt[-4*x + x^2 + 4*y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^4}{4}-\frac {1}{4} (1+4 c_1) x^2+x+c_1{}^2 \\ \end{align*}