Internal problem ID [11686]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} y^{\prime }+y x -y^{3} x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x)+x*y(x)=x*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {c_{1} x^{2}+1}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {c_{1} x^{2}+1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 58
DSolve[x^2*y'[x]+x*y[x]==x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {1+e^{2 c_1} x^2}} \\ y(x)\to \frac {1}{\sqrt {1+e^{2 c_1} x^2}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}