60.1.560 problem 574

Internal problem ID [10574]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 574
Date solved : Sunday, March 30, 2025 at 06:08:06 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 41

ode:=f(x-3/2*diff(y(x),x)^2)+diff(y(x),x)^3-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= f \left (c_1 \right )-\frac {2 \sqrt {6}\, \sqrt {\left (-c_1 +x \right )^{3}}}{9} \\ y &= f \left (c_1 \right )+\frac {2 \sqrt {6}\, \sqrt {\left (-c_1 +x \right )^{3}}}{9} \\ \end{align*}

✓ Mathematica. Time used: 1.434 (sec). Leaf size: 62

ode=f[x - (3*D[y[x],x]^2)/2] - y[x] + D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{9} \left (9 f(c_1)+2 \sqrt {6} (x-c_1){}^{3/2}\right ) \\ y(x)\to \frac {1}{9} \left (9 f(c_1)-2 \sqrt {6} (x-c_1){}^{3/2}\right ) \\ \end{align*}

✗ Sympy

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

NotImplementedError : multiple generators [_X0, f(-3*_X0**2/2 + x)] 
No algorithms are implemented to solve equation _X0**3 + f(-3*_X0**2/2 + x) - y(x)