If y = a sin mx + b cos mx, then \(\frac{d^2y}{dx^2}\) is equal to A

1.	If y = a sin mx + b cos mx, then \(\frac{d^2y}{dx^2}\) is equal to A. –m2y B. m2y C. –my D. my
Answer» Correct Answer is (A) –m²y Given: y = a sin mx + b cos mx \(\frac{dy}{dx}\)= ma cos mx - mb sin mx \(\frac{d^2y}{dx^2}\)= -m² a sin mx - m² b cos mx = -m² [a sin mx + b cos mx] = - m²y

If y = a sin mx + b cos mx, then \(\frac{d^2y}{dx^2}\) is equal to A. –m2y B. m2y C. –my D. my

Answer»

Correct Answer is (A) –m²y

Given:

y = a sin mx + b cos mx

\(\frac{dy}{dx}\)= ma cos mx - mb sin mx

\(\frac{d^2y}{dx^2}\)= -m² a sin mx - m² b cos mx

= -m² [a sin mx + b cos mx]

= - m²y