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If `y=e^(4x) sin3x` , show that `(d^2y)/dx^2-8 dy/dx+25y=0`
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`dy/dx = e^(4x) (cos3x)3+(sin3x)e^(4x)xx4`
`dy/dx = 3e^(4x) cos3x+4y`
`(d^2y)/(dx^2) = -9e^(4x)sin3x+4dy/dx-16y+4dy/dx` [Using ans. of `dy/dx`]
`(d^2y)/(dx^2) = -9y+8dy/dx-16y`
`(d^2y)/(dx^2)-8dy/dx+25y = 0`
So the answer is obtained as required.
Posted by jeew-m on September 16, 2013 at 5:37 AM (Answer #1)
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