Internal problem ID [3614]
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]
\[ \boxed {x \left (-x^{2}+1\right ) y^{\prime }-\left (x^{2}-x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*(-x^2+1)*diff(y(x),x) = (x^2-x+1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x}{\sqrt {x -1}\, \left (x +1\right )^{\frac {3}{2}}} \]
✓ 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}{(x+1) \sqrt {1-x^2}} y(x)\to 0 \end{align*}