28.1.8 problem 8

Internal problem ID [4314]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 8
Date solved : Monday, January 27, 2025 at 09:01:51 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }+\frac {x}{y}+2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 21

dsolve(diff(y(x),x)+x/y(x)+2=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x \left (\operatorname {LambertW}\left (-c_{1} x \right )+1\right )}{\operatorname {LambertW}\left (-c_{1} x \right )} \]

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 31

DSolve[D[y[x],x]+x/y[x]+2==0,y[x],x,IncludeSingularSolutions -> True]
 

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