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The function u=e^x sinx , v=e^x cosx sat...

The function `u=e^x sinx , v=e^x cosx` satisfy the equation (a) `v (du)/(dx)-u(du)/(dx)=u^2+v^2` (b) `(d^2u)/(dx^2)=2v` (c) `d^2v)/(dx^2)=-2u` (d) `(du)/(dx)+(dv)/(dx)=2v`

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Knowledge Check

  • The functions u=e^(x)sinx,v=e^(x)cosx satisfy the equation

    A
    `V(du)/(dx)-u(dv)/(dx)=u^(2)+v^(2)`
    B
    `(d^(2)u)/(dx^(2))=2V`
    C
    `(d^(2)v)/(dx^(2))=-2u`
    D
    `(du)/(dx)+(dv)/(dx)=2v`

  • If u=e^(ax)sinbx and v=e^(ax)cosbx . then what is u(du)/(dx)+v(dv)/(dx) equal to ?

    A
    A) `ae^(2ax)`
    B
    B) `(a^(2)+b^(2))e^(ax)`
    C
    C) `abe^(2ax)`
    D
    D) `(a+b)e^(ax)`

  • int(u(v(du)/(dx)-u(dv)/(dx)))/(v^(3))dx=

    A
    `log((u)/(v))+c`
    B
    `(u^(2)v^(2))/(2)+c`
    C
    `(u^(2))/(2v^(2))+c`
    D
    `(u)/(2v)+c`

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