Internal problem ID [8213]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 2.197 (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)
\[ y \relax (x ) = \RootOf \left (-{\mathrm e}^{\RootOf \left (-343 \left (\tanh ^{2}\left (\frac {\left (4 c_{1}-4 x -3 \textit {\_Z} \right ) \sqrt {7}}{6}\right )\right )+343+98 \,{\mathrm e}^{\textit {\_Z}}\right )}-3+2 \textit {\_Z} +2 \textit {\_Z}^{2}\right ) {\mathrm e}^{\frac {2 x}{3}} \]
✓ Solution by Mathematica
Time used: 0.169 (sec). Leaf size: 85
DSolve[y'[x] == E^((2*x)/3)/(1 + y[x]/E^((2*x)/3)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [7 \left (3 \log \left (-\frac {2}{3} e^{-4 x/3} y(x)^2-\frac {2}{3} e^{-2 x/3} y(x)+1\right )+4 x-9 c_1\right )=6 \sqrt {7} \tanh ^{-1}\left (\frac {y(x)+4 e^{2 x/3}}{\sqrt {7} \left (y(x)+e^{2 x/3}\right )}\right ),y(x)\right ] \]