Internal problem ID [1077]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {a y+b x y+\left (c x +d x y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve((a*y(x)+b*x*y(x))+(c*x+d*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {a \ln \left (x \right )+b x +c \operatorname {LambertW}\left (\frac {d \,x^{-\frac {a}{c}} {\mathrm e}^{-\frac {b x}{c}-\frac {c_{1}}{c}}}{c}\right )+c_{1}}{c}} \]
✓ Solution by Mathematica
Time used: 1.001 (sec). Leaf size: 42
DSolve[(a*y[x]+b*x*y[x])+(c*x+d*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c W\left (\frac {d x^{-\frac {a}{c}} e^{\frac {-b x+c_1}{c}}}{c}\right )}{d} \\ y(x)\to 0 \\ \end{align*}