Internal problem ID [8277]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 697.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 40
dsolve(diff(y(x),x) = (1+y(x)^2*exp(-4/3*x)+y(x)^3*exp(-2*x))*exp(2/3*x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-x +3 \left (\int _{}^{\textit {\_Z}}\frac {1}{3 \textit {\_a}^{3}+3 \textit {\_a}^{2}-2 \textit {\_a} +3}d \textit {\_a} \right )+c_{1}\right ) {\mathrm e}^{\frac {2 x}{3}} \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 114
DSolve[y'[x] == E^((2*x)/3)*(1 + y[x]^2/E^((4*x)/3) + y[x]^3/E^(2*x)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {35}{3} \text {RootSum}\left [-35 \text {$\#$1}^3+9 \sqrt [3]{35} \text {$\#$1}-35\&,\frac {\log \left (\frac {3 e^{-4 x/3} y(x)+e^{-2 x/3}}{\sqrt [3]{35} \sqrt [3]{e^{-2 x}}}-\text {$\#$1}\right )}{3 \sqrt [3]{35}-35 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 35^{2/3} e^{4 x/3} \left (e^{-2 x}\right )^{2/3} x+c_1,y(x)\right ] \]