Question
Asked Nov 18, 2019
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In Exercises 1-31 use the Laplace transform to solve the initial value problem
y (0) 1
y 3y'2y= e',
y'(0)
1.
= -6
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In Exercises 1-31 use the Laplace transform to solve the initial value problem y (0) 1 y 3y'2y= e', y'(0) 1. = -6

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Expert Answer

Step 1

To solve using Laplace transform, first take laplace transform and use the following functions to convert it into function of s.

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L{y s)(0) L{y} = s°r(s)-sy(0)- y'(0)

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Step 2

Take Laplace transformation on both side of the differential equation,

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L{v"+ 3y'+2y}=L{e} L{y+3L{y'}+2L{y} = 1{€ }

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Step 3

Substitute the value of Lap...

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1 fr(s)-sy(0)y(0)+3[sr(s)-y(0)]+2¥ (s) = -1

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Advanced Math