18.1.12 problem Problem 14.14

Internal problem ID [3468]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.14
Date solved : Monday, January 27, 2025 at 07:38:03 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1}{x +2 y+1} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 60.048 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{2} \left (-2 W\left (-\frac {1}{2} c_1 e^{-\frac {x}{2}-\frac {3}{2}}\right )-x-3\right ) \]