Internal problem ID [8298]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 718.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1+{\mathrm e}^{2 x^{2}} y^{2}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x) = (1+y(x)^2*exp(2*x^2)+y(x)^3*exp(3*x^2))*exp(-x^2)*x,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (11 \RootOf \left (-5 x^{2}+20250 \left (\int _{}^{\textit {\_Z}}\frac {1}{121 \textit {\_a}^{3}+3375 \textit {\_a} -3375}d \textit {\_a} \right )+6 c_{1}\right )+15\right ) {\mathrm e}^{-x^{2}}}{45} \]
✓ Solution by Mathematica
Time used: 0.236 (sec). Leaf size: 127
DSolve[y'[x] == (x*(1 + E^(2*x^2)*y[x]^2 + E^(3*x^2)*y[x]^3))/E^x^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {11}{3} \text {RootSum}\left [11 \text {$\#$1}^3+15 \sqrt [3]{11} \text {$\#$1}+11\&,\frac {\log \left (\frac {3 e^{2 x^2} x y(x)+e^{x^2} x}{\sqrt [3]{11} \sqrt [3]{e^{3 x^2} x^3}}-\text {$\#$1}\right )}{11 \text {$\#$1}^2+5 \sqrt [3]{11}}\&\right ]=\frac {11^{2/3} e^{x^2} x^3}{18 \sqrt [3]{e^{3 x^2} x^3}}+c_1,y(x)\right ] \]