​ If y = acosmx + b sinmx, show that d^2y/dx^2 + m^2y = 0 ​

Question

If y = acosmx + b sinmx, show that \(\frac{d^2y}{dx^2}\) + m²y = 0

Answer 1

Given y = acosmx + bsinmx 

\(\frac{dy}{dx}\) = - amsinmx + bmcosmx 

\(\frac{d^2y}{dx^2}\) = - am²cosmx – bm²sinmx 

= m²(acosmx + bsinmx) = -m²y

⇒ \(\frac{d^2y}{dx^2}\)  + m²y = 0