Internal problem ID [8185]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 605.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y^{2} \left (2 x -F \left (-\frac {y x -2}{2 y}\right )\right )}{4 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 43
dsolve(diff(y(x),x) = -1/4*y(x)^2*(2*x-F(-1/2*(-2+x*y(x))/y(x)))/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2}{x +2 \RootOf \left (F \left (\textit {\_Z} \right )\right )} \\ y \relax (x ) = \frac {2}{2 \RootOf \left (-\ln \relax (x )-4 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1}\right )+x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.333 (sec). Leaf size: 145
DSolve[y'[x] == -1/4*((2*x - F[(1 - (x*y[x])/2)/y[x]])*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {2 \left (-\frac {K[1]}{2 K[2]}-\frac {1-\frac {1}{2} K[1] K[2]}{K[2]^2}\right ) F'\left (\frac {1-\frac {1}{2} K[1] K[2]}{K[2]}\right )}{F\left (\frac {1-\frac {1}{2} K[1] K[2]}{K[2]}\right )^2}dK[1]-\frac {4}{F\left (\frac {1-\frac {1}{2} x K[2]}{K[2]}\right ) K[2]^2}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]}-\frac {2}{F\left (\frac {1-\frac {1}{2} K[1] y(x)}{y(x)}\right )}\right )dK[1]=c_1,y(x)\right ] \]