47.1.7 problem 7

Internal problem ID [7388]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:51:42 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 19

dsolve([(x^2-1)*diff(y(x),x)+2*x*y(x)^2=0,y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {1}{-i \pi +\ln \left (x -1\right )+\ln \left (x +1\right )+1} \]

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 26

DSolve[{(x^2-1)*D[y[x],x]+2*x*y[x]^2==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {i}{i \log \left (x^2-1\right )+\pi +i} \]