7.7.32 problem 32

Internal problem ID [210]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 32
Date solved : Monday, January 27, 2025 at 02:41:42 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(x),x)=x*y(x)^3-x*y(x),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: 1.868 (sec). Leaf size: 58

DSolve[D[y[x],x]==x*y[x]^3-x*y[x],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*}