Punjab Technical University 2010-5th Sem B.Sc BioInformatics BI (504) (th) Partial Differtial Equation - Question Paper

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Total No. of Questions : 13]    [Total No. of Pages : 02

Paper ID [C1425]

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B.Sc. BI(504) (S05/Old) (Sem. - 5^th)

PARTIAL DIFFERENTIAL EQUATION Time : 03 Hours    Maximum Marks : 75

Instruction to Candidates:

1)    Section-A is Compulsory.

2)    Attempt any Nine questions from Section-B.

Section - A

Q1)    (15 x 2 = 30)

a) Write the order and degree of the equation

2 2 2 x y z

b)    Obtain a partial differential equation from -y+j-+-y=1.

a b c

c)    Write Geometrical interpretation of Pp + Qq = R in 2-3 lines.

d)    State Charpit method.

e)    Give an example of P.D.E. which can be solved using Charpit method.

f)    Write the General form of Linear Non-homogeneous partial differential equation with constant coefficients.

g)    Define particular integral for P.D.E.

h)    Solve -7 dyy+6 jyl=0 ' dx dxdy dy

d d

i)    Solve DD'(D - 2D'-3)u = 0 whereD = and D' = .

dx    dy

j) Find P.I. of (D² -DD' + D'- 1)z=cos(x + 2y) + e^y.

k) Solve (D² - 9D'²)z = 0 d 2 d 2

l) Solve dr⁺ir2=^12(x + ^y).

'    dx dy

J-8216 [S-9700371]    p.t.o.

m) What is P.I. of F(D, D')z = f (x, y) when f(x, y) = sin(ax+by).

n) Write General form of P.D.E reducible to linear form with constant coefficients.

o) Find particular integral of x² d-^z-y^{2 d}-^zz=xy

dx dy

Section - B    (9 x 5 = 45)

Q2)    Solve (x² - yz)p + (y² - zx)q = z² - xy.

Q3)    Solve 2(z + xp + yq) = yp².

Q4)    Solve (z²- 2yz - y²)p + (xy + zx)q = xy - zx using Lagranges solutions.

Q5)    Solve p - q = z / (x + y)

Q6)    Solve by Charpit method 2(pq + py + qx) + x² + y² = 0

Q7)    Solve p tan x+q tan y = tan z

d³u d³u

3,3

^Q8) Solve -a/ ^{= x y} Q9) Solve (D-D'-1)(D-D'-2)z = e^2x-y + x

Q10) Solve (2D² -5DD'+ 2D'²)z = 24(y -x)

Q11) Solve (D² -DD'-2D)z = sin(3x+4y)-e

Q12) Solve x² dl2+2xy ik+y²1!|=0

dx    dxdy dy

Q13) Solve x²-y-^d22_yHi+xh. = 0.

dx dy dy dx

J-8216 [S-9700371]

Attachment: punjab-technical-university-2010-b-sc-bioinformatics-23456-1.pdf

Earning:   Approval pending.