Internal problem ID [8429]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 849.
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-\sqrt {x^{2}-4 x +4 y}-x^{2} \sqrt {x^{2}-4 x +4 y}-x^{3} \sqrt {x^{2}-4 x +4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.337 (sec). Leaf size: 33
dsolve(diff(y(x),x) = -1/2*x+1+(x^2-4*x+4*y(x))^(1/2)+x^2*(x^2-4*x+4*y(x))^(1/2)+x^3*(x^2-4*x+4*y(x))^(1/2),y(x), singsol=all)
\[ c_{1}+\frac {x^{4}}{2}+\frac {2 x^{3}}{3}+2 x -\sqrt {x^{2}+4 y \relax (x )-4 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.568 (sec). Leaf size: 55
DSolve[y'[x] == 1 - x/2 + Sqrt[-4*x + x^2 + 4*y[x]] + x^2*Sqrt[-4*x + x^2 + 4*y[x]] + x^3*Sqrt[-4*x + x^2 + 4*y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{6} c_1 x \left ((3 x+4) x^2+12\right )+\frac {1}{144} x (3 x+4) \left (3 x^6+4 x^5+24 x^3+36\right )+c_1{}^2 \\ \end{align*}