1st order ivp


by Ry122
Tags: order
Ry122
Ry122 is offline
#1
Mar7-12, 05:15 PM
P: 516
y' = x
x' = -5y-4x

y(0) = 1
x(0) = 0

after finding the general solution as shown here
http://www.wolframalpha.com/input/?i...%27+%3D+-5y-4x

how do you go about applying the initial values and finding the complete solution?
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HallsofIvy
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#2
Mar7-12, 05:24 PM
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PF Gold
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Your general solution should have two undetermined coefficients. Substitute 0 for t, set x= 0, y= 1 and you will have two equations to solve for the two coefficients.
Ry122
Ry122 is offline
#3
Mar7-12, 10:39 PM
P: 516
actually I don't think wolfram alpha has done the correct thing in making x and y a function of t as there's no mention of another variable in the original equations. What would you do when they aren't functions of t?

HallsofIvy
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#4
Mar8-12, 07:13 AM
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PF Gold
P: 38,879

1st order ivp


You can call the independent variable whatever you want! What did you mean by x' and y'? I assumed the primes were derivatives. With respect to what variable?


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