Internal problem ID [3026]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 278.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }+1-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 47
dsolve((-x^2+1)*diff(y(x),x)+1 = x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {\left (x -1\right ) \left (x +1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 30
DSolve[(1-x^2)y'[x]+1==x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1}{\sqrt {x^2-1}} \\ \end{align*}