Internal problem ID [8395]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 815.
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 (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{81 \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: 202
dsolve(diff(y(x),x) = 1/81*(3+y(x))^3*exp(9/2*x^2)*x*exp(3/2*x^2)/(3*exp(3/2*x^2)+exp(3/2*x^2)*y(x)+3*y(x))/exp(3*x^2),y(x), singsol=all)
\[ -10 \ln \left (\frac {10 \,{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \relax (x )\right )}{9 \left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+y \relax (x ) {\mathrm e}^{\frac {3 x^{2}}{2}}+3 y \relax (x )\right )}\right )+5 \ln \left (\frac {\frac {100 \,{\mathrm e}^{3 x^{2}} y \relax (x )^{2}}{189}+\frac {200 \,{\mathrm e}^{3 x^{2}} y \relax (x )}{63}-\frac {300 y \relax (x )^{2} {\mathrm e}^{\frac {3 x^{2}}{2}}}{7}+\frac {100 \,{\mathrm e}^{3 x^{2}}}{21}-\frac {900 y \relax (x ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{7}-\frac {900 y \relax (x )^{2}}{7}}{\left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+y \relax (x ) {\mathrm e}^{\frac {3 x^{2}}{2}}+3 y \relax (x )\right )^{2}}\right )-\frac {30 \sqrt {93}\, \arctanh \left (\frac {\left (29 y \relax (x ) {\mathrm e}^{\frac {3 x^{2}}{2}}+87 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 y \relax (x )\right ) \sqrt {93}}{837 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+279 y \relax (x ) {\mathrm e}^{\frac {3 x^{2}}{2}}+837 y \relax (x )}\right )}{31}+15 x^{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 8.074 (sec). Leaf size: 103
DSolve[y'[x] == (E^(3*x^2)*x*(3 + y[x])^3)/(81*(3*E^((3*x^2)/2) + 3*y[x] + E^((3*x^2)/2)*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{186} \left (31 \log \left (-81 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+e^{3 x^2} (y(x)+3)^2-243 y(x)^2\right )+6 \sqrt {93} \tanh ^{-1}\left (\frac {81 y(x)-2 e^{\frac {3 x^2}{2}} (y(x)+3)}{9 \sqrt {93} y(x)}\right )\right )-\frac {1}{3} \log (y(x)+3)=c_1,y(x)\right ] \]