54.2.153 problem 730

Internal problem ID [12027]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 730
Date solved : Sunday, October 12, 2025 at 02:11:46 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \end{align*}

✓ Maple. Time used: 0.182 (sec). Leaf size: 37

ode:=diff(y(x),x) = 1/4*(2*y(x)^(3/2)-3*exp(x))^3*exp(x)/(2*y(x)^(3/2)-3*exp(x)+2)/y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ {\mathrm e}^{x}-\frac {2 \int _{}^{y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}}\frac {\textit {\_a} +1}{\textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a}}{3}-c_1 = 0 \]

✓ Mathematica. Time used: 0.158 (sec). Leaf size: 56

ode=D[y[x],x] == (E^x*(-3*E^x + 2*y[x]^(3/2))^3)/(4*Sqrt[y[x]]*(2 - 3*E^x + 2*y[x]^(3/2))); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\int _1^{y(x)^{3/2}-\frac {3 e^x}{2}}\frac {2 K[1]+2}{3 K[1]^3-3 K[1]-3}dK[1]+e^x-c_1=0,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(2*y(x)**(3/2) - 3*exp(x))**3*exp(x)/((8*y(x)**(3/2) - 12*exp(x) + 8)*sqrt(y(x))) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out