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Verify that the function y = c(1) e^(ax)...

Verify that the function `y = c_(1) e^(ax) cos bx + c_(2)e^(ax) sin bx`, where `c_(1),c_(2)` are arbitrary constants is a solution of the differential equation
`(d^(2)y)/(dx^(2)) - 2a(dy)/(dx) + (a^(2) + b^(2))y = 0`

Text Solution

Verified by Experts

The correct Answer is:
` = e^(ax)[0 xx sin bx + 0 cos bx] = e^(ax) xx 0 = 0 = R.H.S`
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Knowledge Check

  • The order of the differential equation 2x^(2)(d^(2)y)/dx^(2)-3(dy)/(dx)+y=0 is

    A
    `2`
    B
    `1`
    C
    `0`
    D
    not defined

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