Internal problem ID [8178]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 598.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+F \left (\frac {y}{x}\right )}{x -1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(diff(y(x),x) = (y(x)+F(y(x)/x))/(x-1),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} \right )+\ln \left (x -1\right )-\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 37
DSolve[y'[x] == (F[y[x]/x] + y[x])/(-1 + x),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{F(K[1])+K[1]}dK[1]=\log (1-x)-\log (x)+c_1,y(x)\right ] \]