Internal problem ID [5032]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 35.
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 {2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 33
dsolve((2*x+y(x)+1)-(4*x+2*y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-2 \,{\mathrm e}^{-5 x} {\mathrm e}^{2} {\mathrm e}^{5 c_{1}}\right )-5 x +2+5 c_{1}}+1-2 x \]
✓ Solution by Mathematica
Time used: 60.032 (sec). Leaf size: 26
DSolve[(2*x+y[x]+1)-(4*x+2*y[x]-3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \text {ProductLog}\left (-e^{-5 x-1+c_1}\right )-2 x+1 \\ \end{align*}