Internal problem ID [8427]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 847.
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}-\frac {1}{2}-\sqrt {x^{2}+2 x +1-4 y}-x^{2} \sqrt {x^{2}+2 x +1-4 y}-x^{3} \sqrt {x^{2}+2 x +1-4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.342 (sec). Leaf size: 34
dsolve(diff(y(x),x) = 1/2*x+1/2+(x^2+2*x+1-4*y(x))^(1/2)+x^2*(x^2+2*x+1-4*y(x))^(1/2)+x^3*(x^2+2*x+1-4*y(x))^(1/2),y(x), singsol=all)
\[ c_{1}-\frac {x^{4}}{2}-\frac {2 x^{3}}{3}-2 x -\sqrt {x^{2}-4 y \relax (x )+2 x +1} = 0 \]
✓ Solution by Mathematica
Time used: 0.862 (sec). Leaf size: 47
DSolve[y'[x] == 1/2 + x/2 + Sqrt[1 + 2*x + x^2 - 4*y[x]] + x^2*Sqrt[1 + 2*x + x^2 - 4*y[x]] + x^3*Sqrt[1 + 2*x + x^2 - 4*y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{144} \left (3 x^4+4 x^3+6 x-6-12 c_1\right ) \left (3 x^4+4 x^3+18 x+6-12 c_1\right ) \\ \end{align*}