67.8.43 problem 13.7 (c)

Internal problem ID [16538]
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 : 13.7 (c)
Date solved : Thursday, October 02, 2025 at 01:36:12 PM
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 (1\right )&=1 \\ y^{\prime }\left (1\right )&=9 \\ \end{align*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 11

ode:=3*y(x)*diff(diff(y(x),x),x) = 2*diff(y(x),x)^2; 
ic:=[y(1) = 1, D(y)(1) = 9]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (3 x -2\right )^{3} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 12

ode=3*y[x]*D[y[x],{x,2}]==2*D[y[x],x]^2; 
ic={y[1]==1,Derivative[1][y][1]==9}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (3 x-2)^3 \end{align*}

✗ 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(1): 1, Subs(Derivative(y(x), x), x, 1): 9} 
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