Internal problem ID [8404]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 824.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (x^{3}+y x^{2}+y^{2}\right )}{x^{2} \left (x -1\right ) \left (x +y\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 1.344 (sec). Leaf size: 61
dsolve(diff(y(x),x) = y(x)/x^2/(x-1)*(x^3+x^2*y(x)+y(x)^2)/(x+y(x)),y(x), singsol=all)
\[ \ln \left (\frac {y \relax (x )}{x}\right )-\frac {\ln \left (\frac {x^{2}+x y \relax (x )+y \relax (x )^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {3}\, \arctan \left (\frac {\left (x +2 y \relax (x )\right ) \sqrt {3}}{3 x}\right )}{3}+\ln \relax (x )-\ln \left (x -1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 68
DSolve[y'[x] == (y[x]*(x^3 + x^2*y[x] + y[x]^2))/((-1 + x)*x^2*(x + y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\text {ArcTan}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\log \left (\frac {y(x)}{x}\right )=\log (1-x)-\log (x)+c_1,y(x)\right ] \]