Internal problem ID [3936]
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 8.4, 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 +y-1+\left (2 x +2 y-3\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 29
dsolve((x+y(x)-1)+(2*x+2*y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (2 \,{\mathrm e}^{x} {\mathrm e}^{-4} {\mathrm e}^{-c_{1}}\right )+x -4-c_{1}}+2-x \]
✓ Solution by Mathematica
Time used: 60.019 (sec). Leaf size: 24
DSolve[(x+y[x]-1)+(2*x+2*y[x]-3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\text {ProductLog}\left (-e^{x-1+c_1}\right )-2 x+4\right ) \\ \end{align*}