Question

Use the laplace transform to solve the given initial-value problem. y'' − 6y' 13y = 0, y(0) = 0, y'(0) = −9

Answer 1

The Laplace transformation of given equation is $y=-\frac{9}{2}e^{3t}\sin \left(2t\right)$.

According to the statement

we have given that the equation and we have to find the Laplace transformation of that equation.

So, For this purpose, we know that the

Laplace transformation is an integral transform that converts a function of a real variable to a function of a complex variables.

And the given equation is

y'' − 6y' + 13y = 0, y(0) = 0, y'(0) = −9

To convert into the Laplace transformation

firstly find the single derivative of given equation in the Laplace transformation and put y = -9 in this.

And now find second derivative of given equation in the Laplace transformation.

And and put y = 0 in the given equation.

After the Laplace transformation give value as a Laplace transformation is $y=-\frac{9}{2}e^{3t}\sin \left(2t\right)$.

So, The Laplace transformation of given equation is $y=-\frac{9}{2}e^{3t}\sin \left(2t\right)$.

Learn more about Laplace transformation here

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