54.2.219 problem 796

Internal problem ID [12093]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 796
Date solved : Sunday, October 12, 2025 at 02:15:43 AM
CAS classification : [[_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 156

ode:=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); 
dsolve(ode,y(x), singsol=all);
 

\[ 5 \ln \left (3\right )-5 \ln \left (7\right )+5 \ln \left (\frac {\left (-9 y^{2}-27 y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}-3 \left (y+3\right )^{2} {\mathrm e}^{3 x^{2}}+y^{2}}{\left (\left (y+3\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+3 y\right )^{2}}\right )-\frac {30 \sqrt {93}\, \operatorname {arctanh}\left (\frac {\left (9 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+27 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+29 y\right ) \sqrt {93}}{\left (93 y+279\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+279 y}\right )}{31}-10 \ln \left (\frac {y}{\left (y+3\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+3 y}\right )-15 x^{2}-c_1 = 0 \]

✓ Mathematica. Time used: 5.934 (sec). Leaf size: 218

ode=D[y[x],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])); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{-\frac {e^{3 x^2} x \left (\left (10+3 e^{\frac {3 x^2}{2}}\right ) y(x)+9 e^{\frac {3 x^2}{2}}\right )}{3^{2/3} \sqrt [3]{7} \left (3+e^{\frac {3 x^2}{2}}\right ) \sqrt [3]{-\frac {e^{9 x^2} x^3}{\left (3+e^{\frac {3 x^2}{2}}\right )^3}} \left (\left (3+e^{\frac {3 x^2}{2}}\right ) y(x)+3 e^{\frac {3 x^2}{2}}\right )}}\frac {1}{K[1]^3+\frac {10 \sqrt [3]{-\frac {1}{3}} K[1]}{7^{2/3}}+1}dK[1]=\frac {3}{2} \sqrt [3]{3} 7^{2/3} e^{-6 x^2} \left (-\frac {e^{9 x^2} x^3}{\left (e^{\frac {3 x^2}{2}}+3\right )^3}\right )^{2/3} \left (e^{\frac {3 x^2}{2}}+3\right )^2+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**3*exp(-3*x**2/2)/(3*y(x)*exp(3*x**2/2) + 9*y(x) + 9*exp(3*x**2/2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out