`y=ae^(mx)+b^(-mx)` satisfies which of the following differential equation?
`y=ae^(mx)+b^(-mx)` satisfies which of the following differential equation?
A. `(dy)/(dx)+my=0`
B. `(dy)/(dx)-my=0`
C. `(d^(2)y)/(dx^(2))-m^(2)y=0`
D. `(d^(2)y)/(dx^(2))+m^(2)y=0`
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Given that, `" "y=ae^(mx)+be^(-mx)`
On differentiating both sides w.r.t. x, we get
`" "(dy)/(dx)=mae^(mx)-bme^(-mx)`
Again, differentiating both sides w.r.t. x, we get
`" "(d^(2)y)/(dx^(2))=m^(2)ae^(mx)+bm^(2)e^(-mx)`
`rArr" "(d^(2)y)/(dx^(2))=m^(2)(ae^(mn)+be^(-mn))`
`rArr" "(d^(2)y)/(dx^(2))=m^(2)y`
`rArr" "(d^(2)y)/(dx^(2))-m^(2)y=0`
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