Internal problem ID [9182]
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)]`]]
\[ \boxed {y^{\prime }-\sqrt {x^{2}+2 x +1-4 y}-x^{2} \sqrt {x^{2}+2 x +1-4 y}-x^{3} \sqrt {x^{2}+2 x +1-4 y}=\frac {x}{2}+\frac {1}{2}} \]
✓ Solution by Maple
Time used: 0.141 (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)
\[ c_{1} -\frac {x^{4}}{2}-\frac {2 x^{3}}{3}-2 x -\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.596 (sec). Leaf size: 69
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]
\[ y(x)\to \frac {1}{144} \left (-9 x^8-24 x^7-16 x^6-72 x^5+24 (-4+3 c_1) x^4+96 c_1 x^3-108 x^2+72 (1+4 c_1) x+36-144 c_1{}^2\right ) \]