Internal problem ID [3043]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 296.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (1-x^{2}\right ) y^{\prime }-1+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve((-x^2+1)*diff(y(x),x) = 1-y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (-\operatorname {arctanh}\left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.524 (sec). Leaf size: 39
DSolve[(1-x^2)y'[x]==(1-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \cosh (c_1)-\sinh (c_1)}{\cosh (c_1)-x \sinh (c_1)} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}