Internal problem ID [3628]
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]
\[ \boxed {\left (-x^{4}+1\right ) y^{\prime }-2 x \left (1-y^{2}\right )=0} \]
✓ 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)
\[ y \left (x \right ) = -\tanh \left (\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\ln \left (x +1\right )}{2}+2 c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.818 (sec). Leaf size: 55
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+e^{2 c_1} \left (x^2-1\right )+1}{-x^2+e^{2 c_1} \left (x^2-1\right )-1} y(x)\to -1 y(x)\to 1 \end{align*}