Internal problem ID [3102]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 354.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (1-x^{2}\right ) y^{\prime }-a \,x^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(x*(-x^2+1)*diff(y(x),x) = a*x^2+y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x a \sqrt {\left (x -1\right ) \left (x +1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {x c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 25
DSolve[x(1-x^2)y'[x]==a x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (a \text {ArcSin}(x)+c_1)}{\sqrt {1-x^2}} \\ \end{align*}