Internal problem ID [3106]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 358.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (1-x^{2}\right ) y^{\prime }-\left (x^{2}-x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x*(-x^2+1)*diff(y(x),x) = (x^2-x+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{\sqrt {x -1}\, \left (x +1\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 30
DSolve[x(1-x^2)y'[x]==(1-x+x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x}{\sqrt {1-x} (x+1)^{3/2}} \\ y(x)\to 0 \\ \end{align*}