Question

how to find general solution of:
y'''' + ky = 0
someone please help its urgent..

Answer 1

alternatively

set \(\large y(x)=e^{rx}\) then \(r^4-k=0\)

Answer 2

r u dumb?? do u even know what y'''' means? thi is not how u find roots of an equation
i know what the roots are.. i just dont know the way to find it

Answer 3

if \(k\ge 0\)then \((r^2-k)(r^2+k)=0\)

\(r=\pm \sqrt{k}\) and \(r=\pm i\sqrt{k}\)

\(y(x)=c_1e^{-\sqrt{k}x}+c_2e^{\sqrt{k}x}+c_4\cos \sqrt{kx}+c_5\sin \sqrt{kx}\)