Internal problem ID [8557]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 977.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-y \left (y^{2}+{\mathrm e}^{-x^{2}} y+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 122
dsolve(diff(y(x),x) = y(x)*(y(x)^2+exp(-x^2)*y(x)+exp(-x^2)^2)/exp(-x^2)^2*x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\sqrt {11}\, \tan \left (\RootOf \left (-4 \sqrt {11}\, x^{2}+4 \sqrt {11}\, \ln \left (11\right )+8 \sqrt {11}\, \ln \left (-\frac {36 \sqrt {11}}{11}+36 \tan \left (\textit {\_Z} \right )\right )-4 \sqrt {11}\, \ln \left (\frac {14256 \,{\mathrm e}^{2 x^{2}} \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{25}+\frac {14256 \,{\mathrm e}^{2 x^{2}}}{25}\right )+9 \sqrt {11}\, c_{1}-8 \textit {\_Z} \right )\right )-1\right ) {\mathrm e}^{-x^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.275 (sec). Leaf size: 139
DSolve[y'[x] == E^(2*x^2)*x*y[x]*(E^(-2*x^2) + y[x]/E^x^2 + y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {25}{3} \text {RootSum}\left [-25 \text {$\#$1}^3+24 \sqrt [3]{-1} 5^{2/3} \text {$\#$1}-25\&,\frac {\log \left (\frac {3 e^{2 x^2} x y(x)+e^{x^2} x}{5^{2/3} \sqrt [3]{-e^{3 x^2} x^3}}-\text {$\#$1}\right )}{8 \sqrt [3]{-1} 5^{2/3}-25 \text {$\#$1}^2}\&\right ]=-\frac {5 \sqrt [3]{5} e^{x^2} x^3}{18 \sqrt [3]{-e^{3 x^2} x^3}}+c_1,y(x)\right ] \]