Internal problem ID [35]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 9.
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=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((-x^2+1)*diff(y(x),x) = 2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x +1\right )^{2}}{-x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 22
DSolve[(-x^2+1)*y'[x] == 2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {c_1 (x+1)}{x-1} \\ y(x)\to 0 \\ \end{align*}