Internal problem ID [3934]
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 8.2, 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 {3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 21
dsolve((3*x+2*y(x)+1)-(3*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 x}{2}-\frac {2 \LambertW \left (-\frac {{\mathrm e}^{\frac {1}{4}} {\mathrm e}^{-\frac {25 x}{4}} c_{1}}{4}\right )}{5}+\frac {1}{10} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 30
DSolve[(3*x+2*y[x]+1)-(3*x+2*y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} \left (-4 \text {ProductLog}\left (-e^{-\frac {25 x}{4}-1+c_1}\right )-15 x+1\right ) \\ \end{align*}