Question

Verify that the given function is a solution to the given differential equation.

x^2y´´+5xy´+4y=0 ; y=(-6/x^2) ; x>0

Answer 1

\[\large{y=-6x^{-2}}\]\[y'=12x^{-3}\]\[y''=-36x^{-4}\]
plug them in the equation
\[x^2(-36x^{-4})+5x(12x^{-3})+4(-6x^{-2}) \]=\[-36x^{-2}+60x^{-2} -24x^{-2} \]divide by x^-2
\[-36+60-24 =0\]
so y=6/x^2 is a solution