Internal problem ID [3108]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 360.
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 }-x^{3} \left (1-x^{2}\right )-\left (-2 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 26
dsolve(x*(-x^2+1)*diff(y(x),x) = x^3*(-x^2+1)+(-2*x^2+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = x \left (x -1\right ) \left (x +1\right )+\sqrt {x -1}\, \sqrt {x +1}\, x c_{1} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 26
DSolve[x(1-x^2)y'[x]==x^3(1-x^2)+(1-2 x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (x^2+c_1 \sqrt {1-x^2}-1\right ) \\ \end{align*}