Internal problem ID [3153]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }+\frac {x}{y}=-2} \]
✓ Solution by Maple
Time used: 0.031 (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: 0.125 (sec). Leaf size: 31
DSolve[y'[x]+x/y[x]+2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}+1\right )=-\log (x)+c_1,y(x)\right ] \]