Question

If `y=Asin mx+B cos mx`, then prove that
`(d^2y)/(dx^2)+m^2y=0`

Answer 1

`y = Asinmx+Bcosmx`
`dy/dx = Amcosmx-Bmsinmx`
`(d^2y)/dx^2 = -Am^2sinmx-Bm^2cosmx`
`(d^2y)/dx^2 = -m^2(Asinmx+Bcosmx)`
`(d^2y)/dx^2 = -m^2(y)`
`(d^2y)/dx^2 + m^2(y) = 0`