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Question
The differential equation for which y = acosx + bsinx is a solution, is ______.
Options
`("d"^2y)/("d"x^2) + y` = 0
`("d"^2y)/("d"x^2) - y` = 0
`("d"^2y)/("d"x^2) + ("a" + "b")y` = 0
`("d"^2y)/("d"x^2) + ("a" - "b")y` = 0
Solution
The differential equation for which y = acosx + bsinx is a solution, is `("d"^2y)/("d"x^2) - y` = 0.
Explanation:
The given equation is y = acosx + bsinx
`("d"y)/("d"x)` = – asinx + bcosx
`("d"^2y)/("d"x^2)` = – acosx – bsinx
⇒ `("d"^2y)/("d"x^2)` = – (acosx + bsinx)
⇒ `("d"^2y)/("d"x^2)` = –y
⇒ `("d"y)/("d"x) + y` = 0
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