Internal problem ID [2040]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y-y^{\prime } x y=-6} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(2*(y(x)+3)=x*y(x)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-1-\frac {2 c_{1}}{3}}}{3 x^{\frac {2}{3}}}\right )-3 \]
✓ Solution by Mathematica
Time used: 20.439 (sec). Leaf size: 106
DSolve[2*(y[x]+3)==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -3 \left (1+W\left (\frac {1}{3} \sqrt [3]{-\frac {e^{-3-c_1}}{x^2}}\right )\right ) \\ y(x)\to -3 \left (1+W\left (-\frac {1}{3} \sqrt [3]{-1} \sqrt [3]{-\frac {e^{-3-c_1}}{x^2}}\right )\right ) \\ y(x)\to -3 \left (1+W\left (\frac {1}{3} (-1)^{2/3} \sqrt [3]{-\frac {e^{-3-c_1}}{x^2}}\right )\right ) \\ y(x)\to -3 \\ \end{align*}