29.13.4 problem 358

Internal problem ID [4958]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 358
Date solved : Monday, January 27, 2025 at 09:55:52 AM
CAS classification : [_separable]

\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(x*(-x^2+1)*diff(y(x),x) = (x^2-x+1)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} x}{\sqrt {x -1}\, \left (x +1\right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 30

DSolve[x(1-x^2)D[y[x],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*}