Download PTU B.Sc (Non-Medical) 2020 March 3rd Sem 76905 Differential Equations Question Paper

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Roll No. Total No. of Pages : 02
Total No. of Questions : 09

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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1. Write briefly :
   1. Define exact differential equation.
   2. What is Clairaut’s equation.
   3. Define Cauchy’s linear equation.
   4. Define linear differential equation with variable coefficients.
   5. Define Partial Differential equation.

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   6. Form Partial differential equation by eliminating arbitrary constants from the relation 3z=ax’ + by’
   7. Find general solution of 97 — 125 + 47 = 0.
   8. Write Charpit’s Auxiliary equation.
   9. Find general solution of (D* — 2D?D’) z = 0.
   10. Solve (y—xp) (p—1) =p.

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SECTION-B

2. Solve | y+Z—+— |dx+—(x+xy")dy=0,x>0.
3. Solve the equation y"" + a’y = sec ax by the method of reduction of order.

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4. Find the equation of integral surfaces of (v — z) p + (z — x) ¢ = x — y, which passes through y=2x,z=0
5. Solve by Charpit’s method g = px + q2
6. (—y) (x+2y)+3(—y) (x+y)+(y+2x0) 2 =0

SECTION-C

7. 1. Find the orthogonal trajectories of the semi cubical parabolas ay² =x³, a being the parameter.

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   2. Solve (D*-1)y :2(1—e’2" )7 by method of variation of parameter.
8. 1. Find the equation of surfaces orthogonal to F (z(x + y)², x² —y²) = 0
   2. Find the general solution of (D’ —3D,> D, +4D,’) z=¢" "

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9. 1. Solve (D*—2D+4)y =¢"cos x.
   2. Solve the system of equations %: y,d—J;:—2x+3 V.

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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