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Show that y=Ce^-x is a solution of the d...

Show that `y=Ce^-x` is a solution of the differential equation `dy/dx+y=0`.

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Knowledge Check

  • The general solution of the differential equation (y dx - x dy)/y=0 .

    A
    x y=C'
    B
    x=C y^2'
    C
    y=c x'
    D
    y=C x^2'

  • The solution of the differential equation (dy)/(dx)= 1/(x+y^2) is

    A
    `y=-x^2-2x-2+ce^x`
    B
    `y=x^2+2x+2-ce^x`
    C
    `x=-y^2-2y+2-ce^y`
    D
    `x=-y^2-2y-2+ce^y`

  • The solution of the differential equation x(dy)/(dx)=(y)/(1+logx) is

    A
    `y=logx+C`
    B
    `y=(C )/(1+logx)`
    C
    `y=C(x+logx)`
    D
    `y=C(1+logx)`

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    The solution to the differential equation ydx+(x+x^(2)y)dy=0 is

    Find the general solution of the differential equation (dy)/(dx)-y=cos x .

    Consider the differential equation x(d^2y)/dx^2+2dy/dx-xy+x^2-2=0 .Show that xy=ae^x+be^-x+x^2 is a solution of the given equation.

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