23.4.97 problem 97

Internal problem ID [6399]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 97
Date solved : Tuesday, September 30, 2025 at 02:56:16 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 22

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

\[ y = \frac {x^{2}}{2}+\frac {c_1 \ln \left (x^{2}-c_1 \right )}{2}+c_2 \]

✓ Mathematica. Time used: 0.23 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.614 (sec). Leaf size: 19

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

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