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First Order Differential Equation

DSO_SCHOLARS 10 questions

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Questions in this quiz (10)

  1. 1Classify the following differential equation:

    (e^x)y'+ 3y = x^2y
    1. ASeparable and not linear.
    2. BLinear and not separable.
    3. CBoth separable and linear.
    4. DNeither separable nor linear.
  2. 2Classify the following differential equation:
    ww'(t)+ 3t = 10
    1. ASeparable and not linear.
    2. BLinear and not separable.
    3. CBoth separable and linear.
    4. DNeither separable nor linear.
  3. 3Classify the following differential equation:

    dx/dt = [x + 2xt+cos(t)]/[1+t^2]
    1. ASeparable and not linear.
    2. BLinear and not separable.
    3. CBoth separable and linear.
    4. DNeither separable nor linear.
  4. 4Classify the following differential equation:

    dz/dt = 1 + z + t + zt
    1. ASeparable and not linear.
    2. BLinear and not separable.
    3. CNeither separable nor linear.
    4. DBoth separable and linear.
  5. 5Suppose y is a function of x.
    Which of the following is (d/dx)(x^3y)
    1. A3x^2y + x^3y'(x)
    2. B3x^2y
    3. C3x^2y'(x)
    4. D3x^2y + x^3
  6. 6Identify the functions p(t) and q(t) if the differential equation dx/dt = [x+t^2−2x√t]/t is written in the form dx/dt + p(t)x = q(t).
    1. AIt is not possible to write the equation in the form described.
    2. Bp(t) = 2√t − 1, q(t) = t^2.
    3. Cp(t) = 1−2√t, q(t) = t.
    4. Dp(t) = [2√t−1]/t, q(t) = t.
  7. 7An integrating factor, I(x), is found for the linear differential equation (1 + x^2)y'(x) + xy = 0, and the equation is rewritten as d/dx(I(x)y) = 0.
    Which of the following options is correct?
    1. AI(x) = e^[(x^2)/2]
    2. BI(x) = √(1+x^2)
    3. CI(x) = 1 + x^2
    4. DIt is not possible to find such a function I(x).
  8. 8Which of the following differential equations are equivalent to d/dx(e^xy) = e^xx?
    (More than one may be correct.)
    1. Ae^xy'(x) = e^xx
    2. Be^xy'(x) + e^xy = e^xx
    3. Cy'(x) = x
    4. Dy'(x) = x − y
  9. 9Consider the linear differential equation y'(x) + x/[1+x]y = 1+x.
    The integrating factor is
    1. Ae^x
    2. B[e^x]/[1+x]
    3. Ce^x(1 + x)
    4. De^(x + x^2/2)
  10. 10Find the general solution to the differential equation y'(x) + [x/(1+x)]y = 1+x.

    (In each of the following options C is an arbitrary constant.)
    1. A(1 + Ce^−x)(1 + x)
    2. B1 + x + C
    3. CC( 1 + x)
    4. De^−x(x + x^2/2+C)(1+x)

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Description
Quiz on First Order Differential Equation, created by DSO_SCHOLARS on 07/03/2015.
Language
English
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