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verify that the given function is a solu...

verify that the given function is a solution of the differential equations :
`(dy)/(dx)+sin x = 0, y=cos x + c`.

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verify that the given function is a solution of the differential equations : y''+4y=0, y = A cos 2x-B sin 2x .

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Knowledge Check

  • The solution of differential equation cos x (dy)/(dx)+y sin x =1

    A
    `tanx+tany=k`
    B
    `tanx-tany=k`
    C
    `(tanx)/(tany)=k`
    D
    `tanx.tany=k`

  • The solution of the differential equation (dy)/(dx) +y/x = sin x is

    A
    ` x(y+cos x)= sin x+C`
    B
    ` x (y-cos x) = sin x+C`
    C
    ` x (y cos x)= sin x+C`
    D
    ` x (y- cos x)= cos x+C`

  • The solution of differential equation (dy)/(dx)-3y= sin 2x is

    A
    `y=e^(-3x) ((cos 2x+3 sin 2x)/(13))+c`
    B
    `y= e^(-3x) ((cos 2x- 3 sin 2x)/(13)) +c`
    C
    `ye^(-3x) = -w^(-3x) ((2 cos 2x + 3 sin 2x)/(13))+c`
    D
    None of these

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    In the following questions verify that the given function is a solution of the given differential equation : y = c_(1) sin x + c_(2)cos x , (d^(2)y)/(d x^(2)) +y =0

    verify that the given function is a solution of the differential equations : y''+4y=0, A cos 2x + B sin 2x

    verify that the given function is a solution of the differential equations : (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0, y=e^(x)(sin x + cos x) .

    The solution of the differential equation ( dy ) /( dx) +y/x = cos x is :

    Solution of the differential equation (y+x(dy)/(dx))sin(xy)=cosx is

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