81.4.5 problem 5-6

Internal problem ID [21519]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-6
Date solved : Thursday, October 02, 2025 at 07:46:39 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 29

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

\[ c_1 +\frac {{\mathrm e}^{y}}{y^{3} x -2 y^{2}-4 y-4} = 0 \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 35

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

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

✓ Sympy. Time used: 0.755 (sec). Leaf size: 32

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

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