Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

If = a cos mx + b sin mx, then show that y2 + m2y = 0. - Business Mathematics and Statistics

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Sum

If = a cos mx + b sin mx, then show that y2 + m2y = 0.

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Solution

y = a cos mx + b sin mx

y1 = a `"d"/"dx"` (cos mx) + b `"d"/"dx"` (sin mx)

`[ ∵ "d"/"dx"  (sin "m"x) = cos "m"x "d"/"dx" ("m"x) = (cos "m"x) . "m"]`

= a(-sin mx) . m + b(cos mx) . m

= -am sin mx + bm cos mx

y2 = -am(cos mx) . m + bm(-sin mx) . m

= -am2 cos mx – bm2 sin mx

= -m2 [a cos mx + b sin mx]

= -m2y

∴ y2 + m2y = 0

Concept: Differentiation Techniques
  Is there an error in this question or solution?
Chapter 5: Differential Calculus - Exercise 5.9 [Page 123]

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