44.6.16 problem 16

Internal problem ID [7160]
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 : 16
Date solved : Sunday, March 30, 2025 at 11:49:29 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 30

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

\[ x +\frac {\left (-y^{2}+2 y-2\right ) {\mathrm e}^{y}-c_1}{y^{2}} = 0 \]

✓ Mathematica. Time used: 0.213 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.980 (sec). Leaf size: 26

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

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