73.7.27 problem 27

Internal problem ID [15185]
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
Date solved : Tuesday, January 28, 2025 at 07:40:40 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} 1-\left (2 y+x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 21

dsolve(1-(x+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 36

DSolve[1-(x+2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{y(x)} \int _1^{y(x)}2 e^{-K[1]} K[1]dK[1]+c_1 e^{y(x)},y(x)\right ] \]