Internal problem ID [8992]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 657.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-x^{2} \sqrt {x^{2}-2 x +1+8 y}=-\frac {x}{4}+\frac {1}{4}} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 26
dsolve(diff(y(x),x) = -1/4*x+1/4+x^2*(x^2-2*x+1+8*y(x))^(1/2),y(x), singsol=all)
\[ c_{1} +\frac {4 x^{3}}{3}-\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.741 (sec). Leaf size: 37
DSolve[y'[x] == 1/4 - x/4 + x^2*Sqrt[1 - 2*x + x^2 + 8*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{72} \left (16 x^6-96 c_1 x^3-9 x^2+18 x-9+144 c_1{}^2\right ) \]