75.14.27 problem 353

Internal problem ID [16870]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 353
Date solved : Monday, March 31, 2025 at 03:34:08 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 11

ode:=3*diff(y(x),x)*diff(diff(y(x),x),x) = 2*y(x); 
ic:=y(0) = 1, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (x +3\right )^{3}}{27} \]

✗ Mathematica

ode=3*D[y[x],x]*D[y[x],{x,2}]==2*y[x]; 
ic={y[0]==1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + 3*Derivative(y(x), x)*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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