Internal problem ID [3538]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 282.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x=-a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve((-x^2+1)*diff(y(x),x)+a-x*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {a \sqrt {\left (x -1\right ) \left (x +1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 57
DSolve[(1-x^2)y'[x]+a-x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-a \log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+a \log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1}{2 \sqrt {x^2-1}} \]