## Using Laplace Transforms to Solve Linear Differential Equations

Laplace transforms may be used to solve linear differential equations with constant coefficients by noting the n

^{th}derivative of f(x) is expressed as:

Conseqently, Laplace transforms may be used to solve linear differential equations with constant coefficients as follows:

- Take Laplace transforms of both sides of equation using property above to express derivatives
- Solve for F(s), Y(s), etc.
- Take inverse Laplace transform to attain ultimate solution of equation

Example:

Solve y' − 3y = e

^{3x}, y(0) = 0

Solution:

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