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In the lienar differential equation of ...

In the lienar differential equation of the form `dy/dx+ Py = Q, `

A

Q is a constant

B

Q is a constant or function of x

C

Q is a function of y

D

Q is a function of both x and y

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The correct Answer is:
B
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Knowledge Check

  • Linear differental equation of the form dy/dx + Py = Q where P, Q are functions of x or costants and the coefficient of dy/dx = 1 . Taking e^(int P dx) as Integrating factor the above form reduces to d/dx(ye^(int Pdx))= Qe ^(intPdx). Solution of the equation dy/dx + 2 y tan x = x sin x given y = 0 when x = pi/3 is -

    A
    `y = cos x - 2cos^(2) x`
    B
    `y = sin x - 2 sin ^(2) x`
    C
    `y = cos x - 2 sin ^(2) sin^(2) x`
    D
    `y = sin x - 2 cos ^(2) x`

  • Linear differental equation of the form dy/dx + Py = Q where P, Q are functions of x or costants and the coefficient of dy/dx = 1 . Taking e^(int P dx) as Integrating factor the above form reduces to d/dx(ye^(int Pdx))= Qe ^(intPdx). Solution of the equation cos t dx/dt + x sin t = 1 is -

    A
    `x = csin t + cos t`
    B
    `x+ c + sint+ cos t`
    C
    `x + sin t + c cos t `
    D
    none of these

  • The integrating factor of the differential equation dy/dx + Py = Q is -

    A
    `e^(x)`
    B
    `e^(Px)`
    C
    `e^(intPdx)`
    D
    none of these

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