Internal problem ID [10108]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 8. Exact
differential equations. Page 11
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\frac {2 y x +1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((2*x*y(x)+1)/y(x)+ (y(x)-x)/y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{\LambertW \left (-{\mathrm e}^{x^{2}} c_{1} x \right )} \]
✓ Solution by Mathematica
Time used: 60.12 (sec). Leaf size: 24
DSolve[(2*x*y[x]+1)/y[x]+ (y[x]-x)/y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\text {ProductLog}\left (x \left (-e^{x^2-c_1}\right )\right )} \\ \end{align*}