Internal problem ID [5000]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 2, First order differential equations. Review problems. page 79
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y^{3} x -\left (-x^{2}+1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(2*x*y(x)^3-(1-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {c_{1} +2 \ln \left (x -1\right )+2 \ln \left (x +1\right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {c_{1} +2 \ln \left (x -1\right )+2 \ln \left (x +1\right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 57
DSolve[2*x*y[x]^3-(1-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {\log \left (x^2-1\right )-c_1}} \\ y(x)\to \frac {1}{\sqrt {2} \sqrt {\log \left (x^2-1\right )-c_1}} \\ y(x)\to 0 \\ \end{align*}