73.8.21 problem 13.4 (b)

Internal problem ID [15150]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.4 (b)
Date solved : Thursday, March 13, 2025 at 05:47:50 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Maple. Time used: 0.120 (sec). Leaf size: 11

ode:=3*y(x)*diff(diff(y(x),x),x) = 2*diff(y(x),x)^2; 
ic:=y(0) = 8, D(y)(0) = 6; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (x +4\right )^{3}}{8} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 14

ode=3*y[x]*D[y[x],{x,2}]==2*D[y[x],x]^2; 
ic={y[0]==8,Derivative[1][y][0] ==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} (x+4)^3 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x)*Derivative(y(x), (x, 2)) - 2*Derivative(y(x), x)**2,0) 
ics = {y(0): 8, Subs(Derivative(y(x), x), x, 0): 6} 
dsolve(ode,func=y(x),ics=ics)
 

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