Internal problem ID [3033]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 285.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }+x^{2}+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 60
dsolve((-x^2+1)*diff(y(x),x)+x^2+x*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x +\sqrt {x^{2}-1}\right ) x^{2}}{\sqrt {x^{2}-1}}-x -\frac {\ln \left (x +\sqrt {x^{2}-1}\right )}{\sqrt {x^{2}-1}}+\sqrt {x -1}\, \sqrt {x +1}\, c_{1} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 46
DSolve[(1-x^2)y'[x]+x^2 +x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2-1} \log \left (\sqrt {x^2-1}-x\right )+c_1 \sqrt {x^2-1}-x \\ \end{align*}