Download PTU B.Sc CS-IT 2020 March 2nd Sem 71506 Partial Differentiation And Differential Equations Question Paper

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Roll No. ‘ ‘ ‘ ‘ ‘ ‘ | ‘ ‘ ‘ ‘ Total No. of Pages : 02

Total No. of Questions : 07

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B.Sc. (CS) (2013 & Onwards) (Sem.-2)

PARTIAL DIFFERENTIATION & DIFFERENTIAL EQUATIONS

Subject Code : BCS-201

M.Code : 71506

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 contains SIX questions carrying TEN marks each and students have to attempt any FOUR questions.

SECTION-A

1. Answer the following :
   1. Define interior point and boundary point.

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   2. If f(x,y)= then show that
      Lt f(x,y) does not exist. (x,y)->(0,0)
   3. Discuss the continuity of f(x,y) at (2, 1) where
      f(x,y)= for(x,y)#(0,0)
      0 for(x,y)=(0,0)

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   4. Evaluate Lt e^xy (x,y)->(1,0)
   5. Define linear differential equation.
   6. Define singular solution of a given differential equation.
   7. Define homogeneous differential equation.
   8. Define orthogonal trajectories.

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   9. Define separable equation.
   10. Define the continuity of a function f (x, y) at a point (a, b).

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SECTION-B

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2. State and prove Euler's homogenous theorem.
3. Consider the function f(x,y)= for(x,y)?(0,0). Find the value of A which will make f continuous at origin.
4. If f(x, y)=x^myⁿe^x, then evaluate f_xy, f_x, f_y and f_xx.
5. Find one parameter family solution of y = px + p², where p=dy/dx.
6. Find the power series solution of (x² —1)y''+3xy'—y=0, about x =0.

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7. Find the solution of Legendre’s equation of order n.

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

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