The equations these: dx/dt=−3x−5y, dy/dt=5x+3y What method for solving this system?

Valery Cook 2022-10-15 Answered
The equations these:
d x d t = 3 x 5 y d y d t = 5 x + 3 y
What method for solving this system?
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Answers (2)

driogairea1
Answered 2022-10-16 Author has 16 answers
Consider the following IVP problem:
d x d t = 3 x 5 y d y d t = 5 x + 3 y
with x ( 0 ) = x 0 and y ( 0 ) = y 0 .
Then, Laplace-transform both sides of both equations to get:
s X ( s ) x 0 = 3 X ( s ) 5 Y ( s ) s Y ( s ) y 0 = 5 X ( s ) + 3 Y ( s ) ,
which is an algebraic system for X ( s ) = L s x ( t ) and Y ( s ) = L s y ( t ). Solve for the unknowns using (for example) Gauss elimination and compute the inverse Laplace transfrom to get the solution.
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benatudq
Answered 2022-10-17 Author has 2 answers
The equations may be rewritten
[ x ( t ) y ( t ) ] = [ 3 5 5 3 ] [ x ( t ) y ( t ) ]
or
X ( t ) = A X ( t )
Do you see the analogy with ordinary differential equations?
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