MATH 20D Lecture 23

If then

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7.4 & 7.5 - Inverse Laplace Transform and Solution to IVP

Solve the IVP: $y^{\prime }=ay,y(0)=y_0$

1. Apply Laplace Transform to both sides of the given ODE
   
   
2. Set to derive an algebraic equation. Solve this algebraic equation for
   
   
3. Reverse/Inverse the transform to obtain our soln
   We have so
   So if
   Then our soln

Summary

1. If you see
   Look for
   using
2. If you see
   Use partial fraction decomp