Internal problem ID [8984]
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)]`]]
\[ \boxed {y^{\prime }-x \sqrt {x^{2}-2 x +1+8 y}=-\frac {x}{4}+\frac {1}{4}} \]
✓ 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: 0.569 (sec). Leaf size: 36
DSolve[y'[x] == 1/4 - x/4 + x*Sqrt[1 - 2*x + x^2 + 8*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (4 x^4-(1+16 c_1) x^2+2 x-1+16 c_1{}^2\right ) \]