Question

if y=acosnx+bsinnx, prove that;d^2y/dX^2 +n^2y=0

Answer 1

y=Acosnx+Bsinnx

dxdy=An(−sinnx)+Bn(cosnx)

dx2d2y=−n2Acosnx+n2B(−sinx)

=−n2(Acosnx+Bsinnx)

dx2d2y+n2y=0

Answer 2

$\huge\sf{Hope \: that \: helps}$