47.4.33 problem 36

Internal problem ID [9807]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 36
Date solved : Tuesday, September 30, 2025 at 06:42:19 PM
CAS classification : [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 16

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

\[ y = \frac {\ln \left (c_1 \,x^{3}+3 c_2 \right )}{3} \]

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.626 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (C_{2} + x^{3} \right )}}{3} \]