8.6.32 problem 32 (b)

Internal problem ID [802]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 32 (b)
Date solved : Monday, January 27, 2025 at 03:07:51 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-y x +x y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x) = -x*y(x)+x*y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_1 +1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_1 +1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.871 (sec). Leaf size: 58

DSolve[D[y[x],x] == -x*y[x]+x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {1+e^{x^2+2 c_1}}} \\ y(x)\to \frac {1}{\sqrt {1+e^{x^2+2 c_1}}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}