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Download SGBAU BSc 2019 Summer 2nd Sem Mathematics Differential Equations Ordinary n Partial Question Paper

Download SGBAU (Sant Gadge Baba Amravati university) BSc 2019 Summer (Bachelor of Science) 2nd Sem Mathematics Differential Equations Ordinary n Partial Previous Question Paper

This post was last modified on 10 February 2020

SGBAU BSc Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university


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B.Sc. Part-1 (Semester-II) Examination

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MATHEMATICS

(Differential Equations : Ordinary & Partial)

Paper—III

Time : Three Hours] [Maximum Marks : 60

Note :— (1) Question No. 1 is compulsory. Solve it in ONE attempt only.

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(2) Attempt ONE question from each unit.

Choose the correct alternative :

  1. The roots of the equation (D2 — 4D + 13)y = 0 are :
    1. distinct and real
    2. real and equal
    3. complex and repeated
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    5. None of these
  2. A linear equation of first order is of the form Y' + PY = Q in which ?
    1. P is function of Y
    2. P and Q are function of X
    3. P is function of X and Q is function of Y
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    5. None of these
  3. The condition for the partial differential equation f(x, y, z, p, Q) = 0 and g(x, y, z, p, Q) =0 to be compatible is that :
    1. None of these
  4. The D.E. is called :
    1. Partial differential equation
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    3. Ordinary differential equation
    4. Total differential equation
    5. Linear differential equation
  5. An equation of the form Pp + Qq = R where P, Q, R are the functions of X, Y, Z is called :
    1. Lagrange’s equation
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    3. Jacobi’s equation
    4. Charpit’s equation
    5. Clairaut’s equation
  6. The particular solution of DE W" + PW' + QW = 0 is y = ex iff :
    1. P+Q=0
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    3. 1+P+Q=0
    4. 1-P+Q=0
    5. 1+P+Q=0
  7. The solution of PDE (D — mD')z = 0 is :
    1. z=F(y + mx)
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    3. z=F(y - mx)
    4. None of these
  8. of PDE is :
    1. F(x,y,z, p) =0
    2. F(x,y,z,q) =0
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    4. F(x,y,z,p,q) =0
    5. F(y,z,p,q) =0
  9. The complete integral of F(x, p) = G(y. q) is :
    1. z= ? h(x, a)dx
    2. ? k(y, a)dy
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    4. z= ? h(x, a)dx + ? k(y, a)dy +b
    5. None of these
  10. The DE Mdx + Ndy = 0 is exact iff

UNIT—I

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  1. (a) Show that the D.E. : (sin x sin y — x ey)dy = (ey + cos x - cos y)dx is exact and hence solve it.
    (b) Find the orthogonal trajectory of rn = an cos n?.
  2. (p) Solve the D.E. : (1 + x3)dy + 2xy dx = cot x dx.
    (q) Solve

UNIT—II

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  1. (a) Solve the D.E. (D2 - 4)y = ex
    (b) Solve the D.E. (x2D2 - 3xD - 3)y = x2 sin(log x).
  2. (p) Solve the D.E. (x2D2 — xD + 4)y = cos(log x).
    (q) Solve the D.E.

UNIT—III

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  1. (a) Solve the system of D.E : D2x — 2y = 0 and D2y + 2x = 0.
    (b) Solve the D.E. by variation of parameter.
  2. (p) Solve x2y" + xy' + y = sin(log x) by changing the independent variable X to z = log x.
    (q) Solve the following D.E. by removing the first derivative :

UNIT—IV

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  1. (a) Solve :
    (b) Find the complete integral of z = p2x + q.
  2. (p) Find the general solution of PDE x2p + y2q = (x + y)z.
    (q) Solve the PDE p2 + q2 = k2

UNIT—V

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  1. (a) Solve the D.E. (D2 + 3DD' + 2D'2)z = x +y.
    (b) Solve by Charpits method pxy + pq + qy = yz.
  2. (p) The PDE z = px + qy is compatible with any equation f(x, y, z, p, q) = 0 where f is homogeneous in x, y, z. Prove this.
    (q) Find a real function v of x and y, reducing to zero when y = 0 and satisfying

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