Internal problem ID [8968]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 633.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class C`]]
\[ \boxed {y^{\prime }-\frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}=0} \]
✓ Solution by Maple
Time used: 0.656 (sec). Leaf size: 52
dsolve(diff(y(x),x) = 1/(y(x)*exp(-2/3*x)+1)*exp(2/3*x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (-{\mathrm e}^{\operatorname {RootOf}\left (-343 \tanh \left (\frac {\left (4 c_{1} -4 x -3 \textit {\_Z} \right ) \sqrt {7}}{6}\right )^{2}+343+98 \,{\mathrm e}^{\textit {\_Z}}\right )}-3+2 \textit {\_Z} +2 \textit {\_Z}^{2}\right ) {\mathrm e}^{\frac {2 x}{3}} \]
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 85
DSolve[y'[x] == E^((2*x)/3)/(1 + y[x]/E^((2*x)/3)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [7 \left (3 \log \left (-\frac {2}{3} e^{-4 x/3} y(x)^2-\frac {2}{3} e^{-2 x/3} y(x)+1\right )+4 x-9 c_1\right )=6 \sqrt {7} \text {arctanh}\left (\frac {y(x)+4 e^{2 x/3}}{\sqrt {7} \left (y(x)+e^{2 x/3}\right )}\right ),y(x)\right ] \]