23.1.3 problem 1(c)

Internal problem ID [4093]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(c)
Date solved : Sunday, March 30, 2025 at 02:17:28 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=3*y(x)-2*x+(3*x-2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}+c_1}{3 x -2} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 21

ode=(3*y[x]-2*x)+(3*x-2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^2-c_1}{3 x-2} \]

✓ Sympy. Time used: 0.202 (sec). Leaf size: 12

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

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