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3 years ago

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A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation 0.

a. Show that satisfies the equation for any constant A. b. Show that satisfies the equation for any constant B. c. Show that satisfies the equation for any constants A and B.

1 answer:

navik [9.2K]3 years ago

7 0

Answer: hi your question is poorly written below is the correct question

answer :

a) y1 = Asint, y'1 = Acost , y"1 = -Asint

b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost

c) y = Asint + B cost satisfies the differential equation for any constant A and B

Step-by-step explanation:

y" + y = 0

Proves

a) y1 = Asint, y'1 = Acost , y"1 = -Asint

b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost

c) y3 = y1 + y2 , y'3 = y'1 + y'2, y"3 = y"1 + y"2

∴ y"1 + y1 = -Asint + Asint

y"2 + y2 = -Bcost + Bcost

y"3 - y3 = y"1 + y"2 - ( y1 + y2 )

= y"1 - y1 + y"2 - y2

= -Asint - Asint + ( - Bcost - Bcost ) = 0

Hence we can conclude that y = Asint + B cost satisfies the equation for any constant A and B

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