Internal problem ID [4967]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }+2 y^{2} x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 27
dsolve([(x^2-1)*diff(y(x),x)+2*x*y(x)^2=0,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {i}{\pi +i \ln \left (x -1\right )+i \ln \left (x +1\right )+i} \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 20
DSolve[{(x^2-1)*y'[x]+2*x*y[x]^2==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\log \left (x^2-1\right )-i \pi +1} \\ \end{align*}