Find the constants for given IVP

  • #1
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Homework Statement


Untitled.png


Homework Equations


DifEqs

The Attempt at a Solution



y ' = 4C1e-4xSinX - 4C2e-4xCosX

y'(0) = -1

-1 = 0 - 4C2

Therefore

C2 = 1/4

Not correct. What am I doing wrong?
 

Answers and Replies

  • #2
vela
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You didn't differentiate correctly. You have to use the product rule.
 
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  • #3
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Sigh... obviously. Can't believe I just did that. Thanks!
 
  • #4
Svein
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What am I doing wrong?
  1. [itex] y=c_{1}e^{-4x}cos(x)+c_{2}e^{-4x}sin(x)[/itex]
  2. [itex]y'=c_{1}(-4e^{-4x}cos(x)-e^{-4x}sin(x))+c_{2}(-4e^{-4x}sin(x)+e^{-4x}cos(x)) [/itex]
Now insert for y(0) and y'(0) and solve.
 
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  • #5
HallsofIvy
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Personally, I would find it easier to write the solution as [itex]y= e^{-4x}(C_1 cos(x)+ C_2 sin(x))[/itex].

Then, by the product rule, [itex]y'= -4e^{-4x}(C_1 cos(x)+ C_2 sin(x))+ e^{-4x}(-C_1 sin(x)+ C_2 cos(x))[/itex].
 
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  • #6
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Yeah I got it dudes. I was just being stupid and completely forgot the product rule.

Thanks
 

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