Internal problem ID [3941]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number: Differential equations with Linear Coefficients. Exercise 8.9, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +2 y+\left (y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.227 (sec). Leaf size: 27
dsolve((x+2*y(x))+(y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = 1-\frac {\left (x +2\right ) \left (\LambertW \left (c_{1} \left (x +2\right )\right )+1\right )}{\LambertW \left (c_{1} \left (x +2\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.2 (sec). Leaf size: 143
DSolve[(x+2*y[x])+(y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {(-2)^{2/3} \left (-\left ((x+1) \log \left (-\frac {3 (-2)^{2/3} (x+2)}{y(x)-1}\right )\right )+x \log \left (\frac {3 (-2)^{2/3} (y(x)+x+1)}{y(x)-1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+x+1)}{y(x)-1}\right )+y(x) \left (-\log \left (-\frac {3 (-2)^{2/3} (x+2)}{y(x)-1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+x+1)}{y(x)-1}\right )-1\right )+1\right )}{9 (y(x)+x+1)}=\frac {1}{9} (-2)^{2/3} \log (x+2)+c_1,y(x)\right ] \]