78.8.35 problem 35

Internal problem ID [18154]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 35
Date solved : Thursday, March 13, 2025 at 11:45:27 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x) = diff(y(x),x)*(3*x-2*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: 0.372 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{2} \left (x^2-c_1 \log \left (x^2+c_1\right )+2 c_2\right ) \]

✓ Sympy. Time used: 0.987 (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)
 

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