36.4.5 problem 6

Internal problem ID [6343]
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
Date solved : Monday, January 27, 2025 at 01:57:40 PM
CAS classification : [_separable]

\begin{align*} 2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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 &= \frac {1}{\sqrt {c_1 +2 \ln \left (x -1\right )+2 \ln \left (x +1\right )}} \\ y &= -\frac {1}{\sqrt {c_1 +2 \ln \left (x -1\right )+2 \ln \left (x +1\right )}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 57

DSolve[2*x*y[x]^3-(1-x^2)*D[y[x],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*}