Internal problem ID [8976]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 641.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {1+2 \sqrt {4 y x^{2}+1}\, x^{4}}{2 x^{3}}=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 31
dsolve(diff(y(x),x) = 1/2*(1+2*(4*x^2*y(x)+1)^(1/2)*x^4)/x^3,y(x), singsol=all)
\[ \frac {2 x^{4}+3 c_{1} x -3 \sqrt {4 x^{2} y \left (x \right )+1}}{3 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.331 (sec). Leaf size: 33
DSolve[y'[x] == (1/2 + x^4*Sqrt[1 + 4*x^2*y[x]])/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^6}{9}-\frac {2 c_1 x^3}{3}-\frac {1}{4 x^2}+c_1{}^2 \]