Internal problem ID [4446]
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 8.6, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (2 x +2 y-1\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve((x+y(x))+(2*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (2 \,{\mathrm e}^{x -2-c_{1}}\right )}{2}-x +1 \]
✓ Solution by Mathematica
Time used: 1.056 (sec). Leaf size: 33
DSolve[(x+y[x])+(2*x+2*y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (W\left (-e^{x-1+c_1}\right )-2 x+2\right ) \\ y(x)\to 1-x \\ \end{align*}