Question

In: Advanced Math

Solve the IVP using Laplace transforms x' + y'=e^t -x''+3x' +y =0 x(0)=0, x'(0)=1, y(0)=0

Solve the IVP using Laplace transforms

x' + y'=e^t

-x''+3x' +y =0

x(0)=0, x'(0)=1, y(0)=0

Expert Solution

take laplace

here x(0)=0 and y(0)=0

.

take laplace

here x(0)=0, x'(0)=1, y(0)=0

put the value of y(s)

take partial fraction

.....................(1)

....................(2)

put s=0

.

put s=1

.

put both constant in equation 2

compare coefficient both sides

.

put all constant in equation 1

take inverse lapalce

.

apply inverse laplace rule

so here

and

.

here we have

take inverse lapalce

.

take partial fraction

................(1)

take s=0

take s=1

.

put both constant in equation 1

.

put the value of x(t)

.

final answer is

.

Colby Messinger answered 2 years ago

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