Question

* +0.2 x = cos(4 t), x(0) = 1

solve the IVP using the Laplace approach

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Answer #1

oc+ 0.25 = cos (4) L(S) + L (0.236)= L Ccos (42) SX(5) - X10 +.2 X(5)= s SP+16 5X(5) -1 +0.2X65) = +16 + Xcs) = s (50 716) (5B- .: A= -25 of BLO Lol C= 400 401 5.5+400 - 25/401 + hol 401 55+1 +16. (5+0.2) (5916) = -5/40) + Tols + 400/01 5+ 1/5 522416X(t)= 100 sincept) + cos(4€) له ما -6. E + 316 oما note تا طهے = 3 (sce = بی کا - ) (راهیم راه ترك - های کاتا Scanned with Cawe use partial fraction to findinverse laplace transform.

First we apply laplace transform on both sides of the differential equation then we solve for x(s). For solution x(t) we find inverse laplace transform of x(s).

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solve the IVP using the Laplace approach * +0.2 x = cos(4 t), x(0) = 1
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