Solving y"+9y=H(t-1) with Laplace Transform

Thread starter Fibonacci
Start date Oct 31, 2010
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Laplace Transformation

In summary, the Laplace Transform is a mathematical tool used to solve differential equations by converting a function of time into a function of complex frequency. To solve an equation using this method, the transform must be applied to both sides of the equation, and then the inverse transform is applied to obtain the solution in the time domain. The Laplace Transform of a function is represented by an integral, and it can handle initial conditions by using a Heaviside function. The main advantage of using Laplace Transform is that it simplifies the solution of differential equations, especially for complex and non-homogeneous equations.

Oct 31, 2010

Fibonacci

Hi, just like to check my answer with someone for the this question

calculate y"+9y=H(t-1) y(0)=0 y'(0)=-2 using laplace method
H is heaviside fuction

my solution:

y=cos(3t)-2sin(3t)/3 + H(t-1)/9(H(t-1) + cos (3t-3) )

thanks

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Nov 6, 2010

matematikawan

y(0)=1 for your solution. Not consistent with the given initial value.

What is the Laplace Transform method?

The Laplace Transform is a mathematical tool used to solve differential equations. It converts a function of time into a function of complex frequency, making it easier to solve for the equation's unknown variable.

How do I solve an equation using Laplace Transform?

To solve an equation using Laplace Transform, you must first apply the transform to both sides of the equation. This will convert the equation into an algebraic equation, which can then be solved for the unknown variable. After solving, you must then apply the inverse Laplace Transform to obtain the solution in the time domain.

What is the Laplace Transform of a function?

The Laplace Transform of a function is represented by the integral of the function multiplied by the exponential function e^(-st). This integral is evaluated from 0 to infinity, where s is a complex frequency variable. The result is a function of s, which can then be used to solve the original equation.

How does the Laplace Transform handle initial conditions?

The Laplace Transform can handle initial conditions by incorporating them into the equation in the form of a Heaviside function. This function accounts for the effect of the initial conditions on the solution of the equation.

What is the advantage of using Laplace Transform to solve equations?

The advantage of using Laplace Transform is that it simplifies the solution of differential equations by converting them into algebraic equations. This method is particularly useful for solving complex and non-homogeneous equations, which would be difficult to solve using traditional methods.