Internal problem ID [3540]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 284.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }+y x=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 58
dsolve((-x^2+1)*diff(y(x),x)-x^2+x*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\ln \left (x +\sqrt {x^{2}-1}\right ) x^{2}}{\sqrt {x^{2}-1}}+x +\frac {\ln \left (x +\sqrt {x^{2}-1}\right )}{\sqrt {x^{2}-1}}+\sqrt {x -1}\, \sqrt {x +1}\, c_{1} \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 43
DSolve[(1-x^2)y'[x]-x^2 +x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x^2-1} \log \left (\sqrt {x^2-1}-x\right )+c_1 \sqrt {x^2-1}+x \]