Internal problem ID [3939]
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 8.8, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {x +2 y+\left (3 x +6 y+3\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve((x+2*y(x))+(3*x+6*y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x}{6}} {\mathrm e}^{-\frac {3}{2}} {\mathrm e}^{\frac {c_{1}}{6}}}{2}\right )-\frac {x}{6}-\frac {3}{2}+\frac {c_{1}}{6}}}{2}-\frac {3}{2}-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 5.235 (sec). Leaf size: 43
DSolve[(x+2*y[x])+(3*x+6*y[x]+3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-2 W\left (-e^{-\frac {x}{6}-1+c_1}\right )-x-3\right ) \\ y(x)\to \frac {1}{2} (-x-3) \\ \end{align*}