Solve Differential equation

👨🏻‍🏫 學術台數學

Audrey Hepburn

2009-09-10 3:55 am

Solve the following linear first order differential equation

dy/dx - 7y = sin2x

by the method of undetermined coefficient.

My query is, is the method of undetermined coefficient be used in solving the second order diff. eqt.?

回答 (4)

Prof. Physics

2009-09-24 5:31 am

✔ 最佳答案

Solve for the complementary solution first.

dy/dx - 7y = 0

yh = Ae7x, where A is a constant

Let yp = Bsin2x + Ccos2x

dy/dx = 2(Bcos2x - Csin2x)

Therefore, 2(Bcos2x - Csin2x) - 7(Bsin2x + Ccos2x) = sin2x

(2B - 7C)cos2x - (2C + 7B)sin2x = sin2x

Solving, B = -7/53, C = -2/53

So, y = Ae7x - 1/53 (7sin2x + 2cos2x)

參考: Physics king

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wong

2009-09-11 1:07 am

是一樣的, 先計 homogeneou part, yc
當然可直接用 1st order linear eq 計

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Ivan

2009-09-10 8:49 pm

The method of course can be used to solve 2nd order diff eq.~

http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/ode/second/so_uc/so_uc.html

http://www.sosmath.com/diffeq/second/guessing/guessing.html

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