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 : Tuesday, February 04, 2025 at 12:41:52 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*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

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

DSolve[y[x]==(y[x]*Exp[y[x]]-2*x)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

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