Internal problem ID [4486]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson
10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise
10.11, page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\frac {x y+1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(((x*y(x)+1)/y(x))+((2*y(x)-x)/y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x^{2}}{4}} c_{1} x}{2}\right )} \]
✓ Solution by Mathematica
Time used: 3.618 (sec). Leaf size: 37
DSolve[((x*y[x]+1)/y[x])+((2*y[x]-x)/y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{2 W\left (-\frac {1}{2} x e^{\frac {1}{4} \left (x^2-2 c_1\right )}\right )} \\ y(x)\to 0 \\ \end{align*}