37.2.8 problem 10.3.9 (a)

Internal problem ID [6405]
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)
Date solved : Monday, January 27, 2025 at 02:00:43 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+y x&=x y^{2} \end{align*}

✓ 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)
 

\[ y = \frac {1}{1+{\mathrm e}^{\frac {x^{2}}{2}} c_1} \]

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 31

DSolve[D[y[x],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*}