Internal problem ID [8512]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 932.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(diff(y(x),x) = 1/243*(27*y(x)^3+27*exp(3*x^2)*y(x)+18*exp(3*x^2)*y(x)^2+3*y(x)^3*exp(3*x^2)+27*exp(9/2*x^2)+27*exp(9/2*x^2)*y(x)+9*exp(9/2*x^2)*y(x)^2+exp(9/2*x^2)*y(x)^3)*exp(3*x^2)*x/y(x)/exp(9/2*x^2),y(x), singsol=all)
\[ y \relax (x ) = -\frac {369 \,{\mathrm e}^{\frac {3 x^{2}}{2}}}{123+123 \,{\mathrm e}^{\frac {3 x^{2}}{2}}-136 \RootOf \left (-41 x^{2}-50243409 \left (\int _{}^{\textit {\_Z}}\frac {1}{9248 \textit {\_a}^{3}-1860867 \textit {\_a} +1860867}d \textit {\_a} \right )+27 c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 2.7 (sec). Leaf size: 3303
DSolve[y'[x] == (x*(27*E^((9*x^2)/2) + 27*E^(3*x^2)*y[x] + 27*E^((9*x^2)/2)*y[x] + 18*E^(3*x^2)*y[x]^2 + 9*E^((9*x^2)/2)*y[x]^2 + 27*y[x]^3 + 3*E^(3*x^2)*y[x]^3 + E^((9*x^2)/2)*y[x]^3))/(243*E^((3*x^2)/2)*y[x]),y[x],x,IncludeSingularSolutions -> True]
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