Internal problem ID [13129]
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: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {-\left (x +2 y\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(1-(x+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{-\frac {x}{2}-1}}{2}\right )-\frac {x}{2}-1 \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 30
DSolve[1-(x+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -W\left (-\frac {1}{2} c_1 e^{-\frac {x}{2}-1}\right )-\frac {x}{2}-1 \]