Internal problem ID [9164]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 829.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}}=0} \]
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 34
dsolve(diff(y(x),x) = 1/2*(1+2*(4*x^2*y(x)+1)^(1/2)*x^3+2*x^5*(4*x^2*y(x)+1)^(1/2)+2*x^6*(4*x^2*y(x)+1)^(1/2))/x^3,y(x), singsol=all)
\[ c_{1} +x^{2}+\frac {x^{4}}{2}+\frac {2 x^{5}}{5}-\frac {\sqrt {4 y \left (x \right ) x^{2}+1}}{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.646 (sec). Leaf size: 81
DSolve[y'[x] == (1/2 + x^3*Sqrt[1 + 4*x^2*y[x]] + x^5*Sqrt[1 + 4*x^2*y[x]] + x^6*Sqrt[1 + 4*x^2*y[x]])/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^{10}}{25}+\frac {x^9}{10}+\frac {x^8}{16}+\frac {x^7}{5}+\frac {x^6}{4}-\frac {2 c_1 x^5}{5}-\frac {1}{4} (-1+2 c_1) x^4-\frac {1}{4 x^2}-c_1 x^2+c_1{}^2 \]