Question
Asked Jul 8, 2019
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Use Laplace transforms to find the solution to the intial value problem

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NIH
find the solution of the given initial value problem
y3y+2y= 6(t - 5) + u10(t), y(0) = 0, y'(0)-
11
2
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NIH find the solution of the given initial value problem y3y+2y= 6(t - 5) + u10(t), y(0) = 0, y'(0)- 11 2

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Expert Answer

Step 1

The given initial value problem is

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5)+10(t), y(0)= 0, y'(0)= y3y 2

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Step 2

Take logarithm on both sides of the differential equation as follows.

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L(y +3y'2y)6L(1-5)+L(40 (1)) I -10s -5 s e L(y)+3Ly)2y) I -10s e -5s e + fy(s)y(0)y0)3(sy(s)-y(0))+2y(s)

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Step 3

Apply the initial ...

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-10s e -5s 1 i'y(s)-03sy(s)-0)+2y(s) S S 2 -10s -5 s 1 ys3+2) s23s2 2 S ys)(s+1)(5+2)) -10s e 1 e (5+1)(s+2) s(s+1)(s+2) 2(s+1)(s +2) 1 1 -10s e -5s e s)e 2s (s+1)(s +2) s(s+1)(s+2) s(s+1)(s+2)

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