Question 1025057
{{{d^3y/dx^3 +2d^2y/dx^2 -13dy/dx +10y=0 }}}

Using the D-notation, the differential equation becomes 

{{{(D^3+2D^2-13D+10)y = 0}}}

<==> (D-2)(D-1)(D+5)y = 0, after factorization


==>the general solution is 

{{{highlight(y = Ae^(2x) + Be^x + Ce^(-5x))}}}