Internal problem ID [1988]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], [_Abel, 2nd type, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1}{x +2 y+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 21
dsolve(diff(y(x),x) = 1/(x+2*y(x)+1),y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left (-\frac {c_{1} {\mathrm e}^{-\frac {x}{2}-\frac {3}{2}}}{2}\right )-\frac {x}{2}-\frac {3}{2} \]
✓ Solution by Mathematica
Time used: 67.969 (sec). Leaf size: 34
DSolve[y'[x] == 1/(x+2*y[x]+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-2 \text {ProductLog}\left (-\frac {1}{2} c_1 e^{-\frac {x}{2}-\frac {3}{2}}\right )-x-3\right ) \\ \end{align*}