If $y = {e^{ax}}\sin {\rm{b}}x,$ then $\frac{{{d^2}y}}{{d{x^2}}} - 2a\frac{{dy}}{{dx}} + {a^2}y$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

y = {e^{ax}}\sin \mathrm{b}x,

then

\frac{{{d^2}y}}{{d{x^2}}} - 2a\frac{{dy}}{{dx}} + {a^2}y

is equal to

View answer and explanation

Correct option: C

- {b^2}y

Option C (

- {b^2}y

) is correct because after differentiating the given function twice and substituting back into the given expression, it simplifies to

- {b^2}y

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