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 1 year ago

use laplace transforms to solve ivp x" + 4x' + 3x = 1, x'(0) = 2,...

use laplace transforms to solve ivp x" + 4x' + 3x = 1, x'(0) = 2, x(0) = 1

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve....

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

y''+ 3y'+2y=e^t y(0)=1 y'(0)=-6 Solve using Laplace transforms. Then, solve using undetermined coefficients. Then, solve using...

y''+ 3y'+2y=e^t y(0)=1 y'(0)=-6 Solve using Laplace transforms. Then, solve using undetermined coefficients. Then, solve using variation of parameters.

3. Using the method of Laplace transforms solve the IVP: y'' + 3y'+2y=e2t, y(0)=1, y'(0)=1

using the Laplace transform solve the IVP y'' +4y= 3sin(t) y(0) =1 , y'(0) = -...

using the Laplace transform solve the IVP y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the partial fraction decomposition step. please explain the decomposition clearly.

Solve using Laplace and Inverse Laplace Transforms. Y’’’-y’’-4y’+4y=0 y(0)=1 y’(0)=9 y’’(0)=1

y′ -xe^x = 0 , y(0) = 4 using laplace transforms

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0)...

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0) = 0, y'(0) = 0, y''(0) = 0.

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0 3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1 14. solve the IVP: X'=( 1 2 3) X, X(0)=(0 ##################0 1 4####### -3/8 ##################0 0 1 ########1/4

Use Laplace transforms to solve x''− 7x' + 6x = e^t + δ(t − 2) +...

Use Laplace transforms to solve x''− 7x' + 6x = e^t + δ(t − 2) + δ(t − 4), x(0) = 0, x'(0) = 0.