Internal problem ID [8237]
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)]]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {x}{4}-\frac {1}{4}-x^{2} \sqrt {x^{2}-2 x +1+8 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.36 (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)
\[ c_{1}+\frac {4 x^{3}}{3}-\sqrt {x^{2}-2 x +1+8 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.701 (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]
\begin{align*} y(x)\to \frac {1}{72} \left (4 x^3-3 x+3-12 c_1\right ) \left (4 x^3+3 x-3-12 c_1\right ) \\ \end{align*}