Internal problem ID [152]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 32 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+y x -x y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x) = -x*y(x)+x*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +1}} y \left (x \right ) = -\frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +1}} \end{align*}
✓ Solution by Mathematica
Time used: 1.917 (sec). Leaf size: 58
DSolve[y'[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*}