Download PTU B.Tech 2020 March CSE-IT 2nd Sem BTAM 201 18 Mathematics Ii Question Paper

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Roll No. [] [] [] [] Total No. of Pages : 02

Total No. of Questions : 18

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B.Tech.(CSE)/(EE)/(ME)/(Civil Engg.) (2018 & Onwards) (Sem.-2)

MATHEMATICS-II

Subject Code : BTAM-201-18

M.Code : 76254

Time : 3 Hrs. Max. Marks : 60

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION - B & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

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SECTION-A

Answer briefly :

1. Is the differential equation (cos ydx — sin ydy)=0 exact?
2. Write the Laplace equation in cylindrical coerdinates.
3. Write the 1-D diffusion equation.

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4. Write the Euler’s equation.
5. Convert the equation ax²+by² = 1 into differential equation.
6. Find the integrating factor, which makes the equation (5x² + 12x² + 6y²) dx + 6xydy = 0 exact.
7. Find the solution of the differential equation y''' —3y" —2y =0
8. Is xv+yv_y = v a non-linear PDE?

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9. Check if the PDE 2r—s—t—p + q =0, is parabolic, elliptic or hyperbolic?
10. Define linear ODE.

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SECTION-B

1. Find the power series solution about x = 0, of the differential equation y'" — 4y = 0.

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2. Solve the differential equation y' + 4xy +xy³ = 0.
3. Solve by method of variation of parameters y"' — 2y’ +y = e^x tan x.
4. Solve (D² + DD’ — 6D'²) z =y sin x.

SECTION-C

1. Find the general solution of the Lagrange’s equation 2yzp + zxq = 3xy.

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2. a) Find the complete integral of the PDE p(3 + q) = 2vz.
   b) Find the general solution of the PDE (2D² + DD'-D'² + D - D') z = e^x+y
3. a) Derive D’Alembert’s solution of 1-D wave equation.
   b) Solve y²p² = 3xp +y=0.
4. a) Solve d²y/dx² -5 dy/dx +6y=e^4x.
   

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   b) Solve dy/dx -y=x²+sin3x

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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