Internal problem ID [8221]
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)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1+2 \sqrt {4 y x^{2}+1}\, x^{4}}{2 x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.438 (sec). Leaf size: 26
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)
\[ c_{1}-\frac {\sqrt {4 x^{2} y \relax (x )+1}}{x}+\frac {2 x^{3}}{3} = 0 \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 27
DSolve[y'[x] == (1/2 + x^4*Sqrt[1 + 4*x^2*y[x]])/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-9+4 \left (x^4-3 c_1 x\right ){}^2}{36 x^2} \\ \end{align*}