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Pune University - SY BSc (Sem - I) MATHEMATICS - II (A), April 2010

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Total No. of Questions : 4] P259 [Total No. of Pages : 2 [3717] - 102 S.Y. B.Sc. (Sem. - I) MATHEMATICS (A) : Differential Equations (New Course) Paper - II (A) Time : 2 Hours] [Max. Marks : 40 Instructions to the candidates : 1) Candidates are advised to see the relevant question paper and solve the same. 2) All questions are compulsory. 3) Figures to the right indicate full marks. Q1) Answer the following questions: a) [10] State the order and degree of the equation. d2 y 1 3 dy 1 2 2 = y + . dx dx b) 1 y2 dy Solve + = 0. dx 1 x2 c) Test whether the differential equation is exact or not (3xy2 x2) dx + (3x2y 6y2 1) dy = 0. d) Find the integrating factor of the differential equation (x2 + y2) dx 2xydy = 0. e) Form the differential equation of family of curve y = cx + c2, where c is a constant. f) Find the particular solution of the differential equation [D3 + 3D2 + 3D + 1]y = e x. g) h) d 3y d2 y dy Solve 3 6 2 + 9 = 0. dx dx dx If f(D) xD + 2 and g(D) D + 5 t hen find [ f(D) g(D)] y, where D d . dx P.T.O.

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Additional Info : S.Y. B.Sc. Mathematics (A) (Semister - I) : Differential Equations (Paper - II(A)) (New Course), Pune University
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