44.6.50 problem 50

Internal problem ID [7194]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 50
Date solved : Sunday, March 30, 2025 at 11:50:55 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 25

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

\[ c_1 +\frac {{\mathrm e}^{-y}}{y^{2} x -3 y+3} = 0 \]

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 29

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

\[ \text {Solve}\left [x=\frac {3 (y(x)-1)}{y(x)^2}+\frac {c_1 e^{-y(x)}}{y(x)^2},y(x)\right ] \]

✓ Sympy. Time used: 1.150 (sec). Leaf size: 26

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

\[ C_{1} + x y^{2}{\left (x \right )} e^{y{\left (x \right )}} - 3 \left (y{\left (x \right )} - 1\right ) e^{y{\left (x \right )}} = 0 \]