Find x(t) and Y(t) using Laplace transform. (dx)/(dt)=2x-3y (dy)/(dt)=y-2x x(0)=8 , y(0)=3

Mylo O'Moore 2020-11-09 Answered

Find x(t) and Y(t) using Laplace transform. {dxdt=2x3ydydt=y2x
x(0)=8,y(0)=3

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Expert Answer

liannemdh
Answered 2020-11-10 Author has 106 answers
Step 1 The given pair of equations {dxdt=2x3ydydt=y2x
x(0)=8,y(0)=3 Step 2 Take Laplace transform sxx(0)=2x3y
(s2)x=83y
y=8(s2)x3 ....(1)
syy(0)=y2x
(s1)y=32x ....(2) Put equation (1) in (2) Step 3 (s1)×(8(s2)x3)=32x
8(s1)(s1)(s2)x=96x
((s1)(s2)6)x=8(s1)9
x=8s17s23s4
x=8s17(s4)(s+1) Take partial fractions x=3s4+5s+1 Take inverse Laplace x(t)=5et+3e4t Step 4 dxdt=2x3y
y=10et+6e4t(5et+12e4t)3=15et6e4t3
y(t)=5et2e4t
Therefore, x(t)=5et+3e4t
y(t)=5et2e4t
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