Internal problem ID [13125]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x +2 y}{x +2 y+3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x)=(x+2*y(x))/(x+2*y(x)+3),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2}+\operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {3 x}{2}} {\mathrm e}^{\frac {1}{2}} c_{1}}{2}\right )-\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 3.703 (sec). Leaf size: 41
DSolve[y'[x]==(x+2*y[x])/(x+2*y[x]+3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (-e^{\frac {3 x}{2}-1+c_1}\right )-\frac {x}{2}-\frac {1}{2} y(x)\to \frac {1}{2} (-x-1) \end{align*}