Internal problem ID [5062]
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]
\[ \boxed {y x +y^{\prime }-x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)+x*y(x)=x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{1+{\mathrm e}^{\frac {x^{2}}{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.25 (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*}