60.2.311 problem 889

Internal problem ID [10885]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 889
Date solved : Sunday, March 30, 2025 at 07:19:22 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{{3}/{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \end{align*}

✓ Maple. Time used: 0.166 (sec). Leaf size: 92

ode:=diff(y(x),x) = -1/8*(-8-8*y(x)^3+24*y(x)^(3/2)*exp(x)-18*exp(x)^2-8*y(x)^(9/2)+36*y(x)^3*exp(x)-54*y(x)^(3/2)*exp(x)^2+27*exp(x)^3)*exp(x)/y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (-6 \,{\mathrm e}^{x}+4 y^{{3}/{2}}\right ) \ln \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right )+\left (6 \,{\mathrm e}^{x}-4 y^{{3}/{2}}\right ) \ln \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )+\left (6 c_1 -6 \,{\mathrm e}^{x}\right ) y^{{3}/{2}}-9 \,{\mathrm e}^{x} c_1 +9 \,{\mathrm e}^{2 x}-4}{-6 y^{{3}/{2}}+9 \,{\mathrm e}^{x}} = 0 \]

✓ Mathematica. Time used: 1.145 (sec). Leaf size: 68

ode=D[y[x],x] == -1/8*(E^x*(-8 - 18*E^(2*x) + 27*E^(3*x) + 24*E^x*y[x]^(3/2) - 54*E^(2*x)*y[x]^(3/2) - 8*y[x]^3 + 36*E^x*y[x]^3 - 8*y[x]^(9/2)))/Sqrt[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}\right )+e^x=\frac {4}{9 e^x-6 y(x)^{3/2}}+\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}+1\right )+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-8*y(x)**(9/2) - 54*y(x)**(3/2)*exp(2*x) + 24*y(x)**(3/2)*exp(x) + 36*y(x)**3*exp(x) - 8*y(x)**3 + 27*exp(3*x) - 18*exp(2*x) - 8)*exp(x)/(8*sqrt(y(x))) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(8*y(x)**(9/2) + 54*y(x)**(3/2)*exp(2*x) - 24*y(x)**(3/2)*exp(x) - 36*y(x)**3*exp(x) + 8*y(x)**3 - 27*exp(3*x) + 18*exp(2*x) + 8)*exp(x)/(8*sqrt(y(x))) + Derivative(y(x), x) cannot be solved by the factorable group method