Internal problem ID [8558]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 978.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (y^{2}+x y+x^{2}+x \right )}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.088 (sec). Leaf size: 71
dsolve(diff(y(x),x) = y(x)/x^2*(y(x)^2+x*y(x)+x^2+x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {3}\, x \tan \left (\RootOf \left (-\sqrt {3}\, \ln \relax (3)-\sqrt {3}\, \ln \left (\frac {4}{3 \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )}\right )-2 \sqrt {3}\, \ln \left (-\frac {\sqrt {3}}{6}+\frac {\tan \left (\textit {\_Z} \right )}{2}\right )+2 \sqrt {3}\, c_{1}+2 \sqrt {3}\, x +2 \textit {\_Z} \right )\right )}{2}-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 60
DSolve[y'[x] == (y[x]*(x + x^2 + x*y[x] + y[x]^2))/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {\text {ArcTan}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\log \left (\frac {y(x)}{x}\right )=x+c_1,y(x)\right ] \]