Internal problem ID [8273]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 693.
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}^{-2 x b}+y^{3} {\mathrm e}^{-3 x b}\right ) {\mathrm e}^{x b}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 40
dsolve(diff(y(x),x) = (1+y(x)^2*exp(-2*b*x)+y(x)^3*exp(-3*b*x))*exp(b*x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-x -\left (\int _{}^{\textit {\_Z}}-\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}-b \textit {\_a} +1}d \textit {\_a} \right )+c_{1}\right ) {\mathrm e}^{b x} \]
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 146
DSolve[y'[x] == E^(b*x)*(1 + y[x]^2/E^(2*b*x) + y[x]^3/E^(3*b*x)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{3} (9 b+29)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (9 b+29)^{2/3}-9 \text {$\#$1} b-3 \text {$\#$1}+(9 b+29)^{2/3}\&,\frac {\log \left (\frac {3 e^{-2 b x} y(x)+e^{-b x}}{\sqrt [3]{(9 b+29) e^{-3 b x}}}-\text {$\#$1}\right )}{\text {$\#$1}^2 \left (-(9 b+29)^{2/3}\right )+3 b+1}\&\right ]=\frac {1}{9} x e^{2 b x} \left ((9 b+29) e^{-3 b x}\right )^{2/3}+c_1,y(x)\right ] \]