Internal problem ID [4554]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order.
page 315
Problem number: 10.3.9 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y+y^{\prime }-y^{2} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
dsolve(diff(y(x),x)+x*y(x)=x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{1+{\mathrm e}^{\frac {x^{2}}{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 31
DSolve[y'[x]+x*y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{1+e^{\frac {x^2}{2}+c_1}} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}