# ODE6.1

From Example Problems

Let

At this point all the information from the IC's are encoded into the transform. Solve for .

Find the partial fraction decomposition of

Multiply both sides by the common denominator.

Compare coefficients.

Solve this system of equations. The augmented matrix has equations as rows and variables as columns. The last column is the value of each equation.

So

So

Use the tables here to find the inverse Laplace transforms.