Internal problem ID [8227]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 649.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }+\frac {x}{4}-\frac {1}{4}-x \sqrt {x^{2}+8 y-2 x +1}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 27
dsolve(diff(y(x),x) = -1/4*x+1/4+x*(x^2-2*x+1+8*y(x))^(1/2),y(x), singsol=all)
\[ c_{1} +\frac {x^{2}}{8}+\frac {17}{128}-\frac {\sqrt {x^{2}-2 x +1+8 y \left (x \right )}}{16} = 0 \]
✓ Solution by Mathematica
Time used: 0.58 (sec). Leaf size: 34
DSolve[y'[x] == 1/4 - x/4 + x*Sqrt[1 - 2*x + x^2 + 8*y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (2 x^2+x-1-4 c_1\right ) (x (2 x-1)+1-4 c_1) \\ \end{align*}