Internal problem ID [8376]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 796.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{3 \left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+{\mathrm e}^{\frac {3 x^{2}}{2}} y+3 y\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 143
dsolve(diff(y(x),x) = 1/3*y(x)^3*x*exp(3*x^2)/(3*exp(3/2*x^2)+exp(3/2*x^2)*y(x)+3*y(x))/exp(9/2*x^2),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\left (7 \,{\mathrm e}^{3 x^{2}+\RootOf \left ({\mathrm e}^{3 x^{2}} \left (42 \sqrt {93}\, \tanh \left (\frac {\left (c_{1}-5 \textit {\_Z} \right ) \sqrt {93}}{90}\right ) {\mathrm e}^{3 x^{2}+\textit {\_Z}}+217 \left (\tanh ^{2}\left (\frac {\left (c_{1}-5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )\right ) {\mathrm e}^{3 x^{2}+\textit {\_Z}}+189 \,{\mathrm e}^{3 x^{2}+\textit {\_Z}}-93 \left (\tanh ^{2}\left (\frac {\left (c_{1}-5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )\right )+93\right )\right )}+9 \,{\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {3 x^{2}}{2}}-3\right ) \textit {\_Z}^{2}+81+\left (54 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81\right ) \textit {\_Z} \right ) {\mathrm e}^{\frac {3 x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 7.64 (sec). Leaf size: 109
DSolve[y'[x] == (x*y[x]^3)/(3*E^((3*x^2)/2)*(3*E^((3*x^2)/2) + 3*y[x] + E^((3*x^2)/2)*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{62} \left (-31 \log \left (9 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+3 e^{3 x^2} (y(x)+3)^2-y(x)^2\right )+6 \sqrt {93} \tanh ^{-1}\left (\frac {\sqrt {\frac {3}{31}} \left (2 e^{\frac {3 x^2}{2}} (y(x)+3)+3 y(x)\right )}{y(x)}\right )+62 \log \left (e^{\frac {3 x^2}{2}}\right )\right )+\log (y(x))=c_1,y(x)\right ] \]