Internal problem ID [9114]
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]
\[ \boxed {y^{\prime }-\frac {y x^{3}+x^{3}+y^{2} x +y^{3}}{\left (x -1\right ) x^{3}}=0} \]
✓ Solution by Maple
Time used: 0.109 (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)
\[ \frac {\ln \left (\frac {x +y \left (x \right )}{x}\right )}{2}-\frac {\ln \left (\frac {y \left (x \right )^{2}+x^{2}}{x^{2}}\right )}{4}+\frac {\arctan \left (\frac {y \left (x \right )}{x}\right )}{2}-\ln \left (x -1\right )+\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.13 (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]
\[ \text {Solve}\left [\frac {1}{2} \arctan \left (\frac {y(x)}{x}\right )-\frac {1}{4} \log \left (\frac {y(x)^2}{x^2}+1\right )+\frac {1}{2} \log \left (\frac {y(x)}{x}+1\right )=\log (1-x)-\log (x)+c_1,y(x)\right ] \]