Initial value problem with a delta term {x'=3x-y+delta(t-1), y'=x+y x(0)=y(0)=1

Darius Miles

Darius Miles

Answered question

2022-09-26

Initial value problem with a delta term
{ x = 3 x y + δ ( t 1 ) y = x + y
x ( 0 ) = y ( 0 ) = 1

Answer & Explanation

ticotaku86

ticotaku86

Beginner2022-09-27Added 12 answers

For t < 1, the delta function term is zero, and the set of equations reduces to the system you already know how to solve. Likewise on the domain 1 < t. Find the general solution on either side of t = 1, then apply the proper matching conditions at t = 1 to determine the remaining undetermined coefficients. (Note that the first derivative will have a jump discontinuity at this point.)

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