60.7.127 problem 1742 (book 6.151)

Internal problem ID [11677]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1742 (book 6.151)
Date solved : Wednesday, March 05, 2025 at 02:40:03 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} 2 y^{\prime \prime } y-3 {y^{\prime }}^{2}-4 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 22

ode:=2*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2-4*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {4}{\left (\sin \left (x \right ) c_{1} -\cos \left (x \right ) c_{2} \right )^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.583 (sec). Leaf size: 44

ode=-4*y[x]^2 - 3*D[y[x],x]^2 + 2*y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 \exp \left (\int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+4}dK[1]\&\right ]\left [c_1+\frac {K[2]}{2}\right ]dK[2]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x)**2 + 2*y(x)*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(6)*sqrt((-2*y(x) + Derivative(y(x), (x, 2)))*y(x))/3 + Derivative(y(x), x) cannot be solved by the factorable group method