Internal problem ID [5720]
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]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 20
dsolve([(x^2-1)*diff(y(x),x)+2*x*y(x)^2=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{-i \pi +\ln \left (x -1\right )+\ln \left (x +1\right )+1} \]
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 26
DSolve[{(x^2-1)*y'[x]+2*x*y[x]^2==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {i}{i \log \left (x^2-1\right )+\pi +i} \]