60.7.134 problem 1749 (book 6.158)

Internal problem ID [11684]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1749 (book 6.158)
Date solved : Sunday, March 30, 2025 at 08:41:59 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 67

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

\begin{align*} y &= 0 \\ -\frac {4 \sqrt {c_1 y^{{3}/{2}}+4 y}}{\sqrt {y}\, c_1}-x -c_2 &= 0 \\ \frac {4 \sqrt {c_1 y^{{3}/{2}}+4 y}}{\sqrt {y}\, c_1}-x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.343 (sec). Leaf size: 43

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

\[ y(x)\to \frac {\left (c_1{}^2 x^2+2 c_2 c_1{}^2 x-64+c_2{}^2 c_1{}^2\right ){}^2}{256 c_1{}^2} \]

✗ Sympy

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

NotImplementedError : The given ODE -2*sqrt(3)*sqrt((Derivative(y(x), (x, 2)) + 1)*y(x))/3 + Derivative(y(x), x) cannot be solved by the factorable group method