88.12.26 problem 28

Internal problem ID [24082]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 28
Date solved : Thursday, October 02, 2025 at 09:58:58 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \left (2+3 y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 25

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

\begin{align*} y &= -{\frac {2}{3}} \\ \frac {\left (3 y+2\right )^{{2}/{3}}}{2}-c_1 x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.521 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to \frac {2}{3} \left (-1+\sqrt {2} (c_1 (x+c_2)){}^{3/2}\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -sqrt((3*y(x) + 2)*Derivative(y(x), (x, 2))) + Derivative(y(x),