60.7.22 problem 1612 (6.22)

Internal problem ID [11572]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1612 (6.22)
Date solved : Sunday, March 30, 2025 at 08:28:34 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x)-y(x)^(3/2)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=12*y[x] - y[x]^(3/2) - 7*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**(3/2) + 12*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE y(x)**(3/2)/7 - 12*y(x)/7 + Derivative(y(x), x) - Derivative(y(x), (x, 2))/7 cannot be solved by the factorable group method