73.7.23 problem 23

Internal problem ID [15181]
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
Date solved : Tuesday, January 28, 2025 at 07:40:27 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 y+x}{x +2 y+3} \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 19

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

\[ y = -\frac {x}{2}+\operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{\frac {3 x}{2}+\frac {1}{2}}}{2}\right )-\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 3.207 (sec). Leaf size: 41

DSolve[D[y[x],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*}