Internal problem ID [3552]
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]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }+y^{2}=1} \]
✓ 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: 0.589 (sec). Leaf size: 47
DSolve[(1-x^2)y'[x]==(1-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x+e^{2 c_1} (x-1)+1}{-x+e^{2 c_1} (x-1)-1} y(x)\to -1 y(x)\to 1 \end{align*}