Internal problem ID [8359]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 779.
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 x^{3}+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 50
dsolve(diff(y(x),x) = 1/(x-1)*(x^3*y(x)+x^3+x*y(x)^2+y(x)^3)/x^3,y(x), singsol=all)
\[ \frac {\ln \left (\frac {y \relax (x )+x}{x}\right )}{2}-\frac {\ln \left (\frac {x^{2}+y \relax (x )^{2}}{x^{2}}\right )}{4}+\frac {\arctan \left (\frac {y \relax (x )}{x}\right )}{2}+\ln \relax (x )-\ln \left (x -1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 57
DSolve[y'[x] == (x^3 + x^3*y[x] + x*y[x]^2 + y[x]^3)/((-1 + x)*x^3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \text {ArcTan}\left (\frac {y(x)}{x}\right )-\frac {1}{4} \log \left (\frac {y(x)^2}{x^2}+1\right )+\frac {1}{2} \log \left (\frac {y(x)}{x}+1\right )=\log (1-x)-\log (x)+c_1,y(x)\right ] \]