Internal problem ID [5785]
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`]]
\[ \boxed {y-\left (4 x +2 y-3\right ) y^{\prime }=-2 x -1} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-5 x} {\mathrm e}^{2} {\mathrm e}^{5 c_{1}}\right )-5 x +2+5 c_{1}}+1-2 x \]
✓ Solution by Mathematica
Time used: 11.239 (sec). Leaf size: 35
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} W\left (-e^{-5 x-1+c_1}\right )-2 x+1 y(x)\to 1-2 x \end{align*}