Internal problem ID [3120]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 372.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x^{4}\right ) y^{\prime }-2 x \left (1-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve((-x^4+1)*diff(y(x),x) = 2*x*(1-y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (x +1\right )}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+2 c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.739 (sec). Leaf size: 43
DSolve[(1-x^4)y'[x]==2 x(1-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \cosh (c_1)-\sinh (c_1)}{\cosh (c_1)-x^2 \sinh (c_1)} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}