Internal problem ID [3610]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 354.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x \left (-x^{2}+1\right ) y^{\prime }-y=a \,x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(x*(-x^2+1)*diff(y(x),x) = a*x^2+y(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x a \sqrt {\left (x -1\right ) \left (x +1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {x c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 42
DSolve[x(1-x^2)y'[x]==a x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x \left (-2 a \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )+c_1\right )}{\sqrt {1-x^2}} \]