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 : Tuesday, February 04, 2025 at 12:46:37 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

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

DSolve[y[x]+(2*x+x*y[x]-3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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