Internal problem ID [9150]
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`]]
\[ \boxed {y^{\prime }-\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{81 \left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+{\mathrm e}^{\frac {3 x^{2}}{2}} y+3 y\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 165
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)
\[ 5 \ln \left (3\right )-5 \ln \left (7\right )+5 \ln \left (\frac {\left (-81 y \left (x \right )^{2}-243 y \left (x \right )\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+\left (3+y \left (x \right )\right )^{2} {\mathrm e}^{3 x^{2}}-243 y \left (x \right )^{2}}{\left ({\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )+3 y \left (x \right )\right )^{2}}\right )-\frac {30 \sqrt {93}\, \operatorname {arctanh}\left (\frac {\left (29 y \left (x \right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+87 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 y \left (x \right )\right ) \sqrt {93}}{\left (279 y \left (x \right )+837\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+837 y \left (x \right )}\right )}{31}-10 \ln \left (\frac {{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )}{{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )+3 y \left (x \right )}\right )+15 x^{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 7.811 (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]
\[ \text {Solve}\left [\frac {1}{186} \left (6 \sqrt {93} \text {arctanh}\left (\frac {81 y(x)-2 e^{\frac {3 x^2}{2}} (y(x)+3)}{9 \sqrt {93} y(x)}\right )+31 \log \left (-81 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+e^{3 x^2} (y(x)+3)^2-243 y(x)^2\right )\right )-\frac {1}{3} \log (y(x)+3)=c_1,y(x)\right ] \]