Control system Laplace

[Chocolatecat]

how to obtain x(t)

 

[pierreick]

Wow! it looks like homework; what will you do the day of the exam?
Good to share your work and explain your difficulties.
Try this calculator, others available.

Wolfram|Alpha Examples: Differential Equations

Answers to differential equations problems. Solve ODEs, linear, nonlinear, ordinary and numerical differential equations, Bessel functions, spheroidal functions.

www.wolframalpha.com

You may want to use Laplace transform

IVP using Laplace ODE Calculator

Free IVP using Laplace ODE Calculator - solve ODE IVP's with Laplace Transforms step by step

www.symbolab.com

Solve the equation for U[t]=1 and x(0) =x'(0) =0

well known curve for linear system.



Pierre

 

[georgeverghese]

I worked this out and my solution to this is x(t) = -(t^2)/2 +2t - 2 +2.e^-t. Dont see why you'd have problems with solving this.
Where exactly do you need help with this ?

 

[pierreick]

Hi,
A tutorial to support your query,

Differential Equations - Second Order DE's

In this chapter we will start looking at second order differential equations. We will concentrate mostly on constant coefficient second order differential equations. We will derive the solutions for homogeneous differential equations and we will use the methods of undetermined coefficients and...

tutorial.math.lamar.edu

Note:
In your case, consider 2nd order autonomous differential equation.
Pierre

 

[pierreick]

Hi,
Another way to write the solution: