Internal problem ID [8235]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 655.
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 {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 2.625 (sec). Leaf size: 64
dsolve(diff(y(x),x) = y(x)^3/(y(x)*exp(-2/3*x)+1)*exp(-4/3*x),y(x), singsol=all)
\[ x +\frac {3 \sqrt {7}\, \arctanh \left (\frac {\left (6 y \relax (x ) {\mathrm e}^{-\frac {2 x}{3}}-2\right ) \sqrt {7}}{14}\right )}{14}-\frac {3 \ln \left (3 y \relax (x )^{2} {\mathrm e}^{-\frac {4 x}{3}}-2 y \relax (x ) {\mathrm e}^{-\frac {2 x}{3}}-2\right )}{4}+\frac {3 \ln \left (y \relax (x ) {\mathrm e}^{-\frac {2 x}{3}}\right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 9.35 (sec). Leaf size: 89
DSolve[y'[x] == y[x]^3/(E^((4*x)/3)*(1 + y[x]/E^((2*x)/3))),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {3}{2} \log (y(x))+\frac {3}{28} \left (-\left (7+\sqrt {7}\right ) \log \left (-\sqrt {7} y(x)+y(x)+2 e^{2 x/3}\right )+\left (\sqrt {7}-7\right ) \log \left (\sqrt {7} y(x)+y(x)+2 e^{2 x/3}\right )+14 \log \left (e^{2 x/3}\right )\right )=c_1,y(x)\right ] \]