2132worksheet3

# 2132worksheet3 - possible(a r 1 = 2,r 2 =-1(b r 1 = 2 i,r 2...

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Polytechnic Institute of NYU MA 2132 Worksheet 3 NOT COLLECTED (1) Find the solution of the diﬀerential equation. (a) 3 xy 00 + 2 y 0 = 0 Answer: y = C 1 + C 2 x 1 3 (b) 4 x 2 y 00 - y = 0 Answer: y = C 1 x 1 2 + C 2 x - 1 2 (c) x 2 y 00 + 4 xy 0 + 2 y = 0, y (1) = 1, y 0 (1) = 2 Answer: y = 4 x - 1 - 3 x - 2

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Your signature: (2) Find a diﬀerential equation of the form P ( D ) y = 0, with real coeﬃcients, whose associated polynomial P has the given numbers among its zeros. The order of P should be as low as
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Unformatted text preview: possible. (a) r 1 = 2 ,r 2 =-1 (b) r 1 = 2 i,r 2 =-1 ,r 3 = 2 Your signature: (3) Find the solution of the given system of diﬀerential equation. (a) y 00 + 2 y + y = 4 e-x ln x Answer: ( C 1 + C 2 x ) e-x + x 2 e-x (2 ln x-3) (b) 4 y 00 + y = sec x 2 . Answer: C 1 cos x 2 + C 2 sin x 2 + cos x 2 ln (cos x 2 ) + 1 2 x sin x 2...
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2132worksheet3 - possible(a r 1 = 2,r 2 =-1(b r 1 = 2 i,r 2...

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