23.1.535 problem 525

Internal problem ID [5142]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 525
Date solved : Tuesday, September 30, 2025 at 11:44:13 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 29

ode:=(2+3*x-x*y(x))*diff(y(x),x)+y(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: 0.057 (sec). Leaf size: 83

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

\[ \text {Solve}\left [x=\exp \left (\int _1^{y(x)}\frac {K[1]-3}{K[1]}dK[1]\right ) \int _1^{y(x)}-\frac {2 \exp \left (-\int _1^{K[2]}\frac {K[1]-3}{K[1]}dK[1]\right )}{K[2]}dK[2]+c_1 \exp \left (\int _1^{y(x)}\frac {K[1]-3}{K[1]}dK[1]\right ),y(x)\right ] \]

✓ Sympy. Time used: 0.746 (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)
 

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