Transcription of Solving Differential Equations
{{id}} {{{paragraph}}}
Example: bachelor of science
Solving Differential Equations
Solving DifferentialEquations this Section we employ the laplace transform to solve constant coefficient ordinary differentialequations. In particular we shall consider initial value problems. We shall find that the initialconditions are automatically included as part of the solution process. The idea is simple; the Laplacetransform of each term in the Differential equation is taken. If the unknown function isy(t)then, ontaking the transform , an algebraic equation involvingY(s) =L{y(t)}is obtained. This equation issolved forY(s)which is then inverted to produce the required solutiony(t) =L 1{Y(s)}.'&$%PrerequisitesBefore starting this Section you should.. understand how to find laplace transforms ofsimple functions and of their derivatives be able to find inverse laplace transformsusing a variety of techniques know what an initial-value problem is Learning OutcomesOn completion you should be able to.. solve initial-value problems using the Laplacetransform method34 HELM (2008):Workbook 20: laplace Transforms 1.
the inverse Laplace transform: y(t) = L−1{Y(s)} = L−1{1 s+1}−L−1{s+1 (s+1)2 +1} = (e−t −e−t cost)u(t) which is the solution to the initial value problem. Exercises Use Laplace transforms to solve: 1. dx dt +x = 9e2t x(0) = 3 2. d2x dt2 +x = 2t x(0) = 0 x0(0) = 5 Answers 1. x(t) = 3e2t 2. x(t) = 3sint+2t 38 HELM (2008): Workbook 20 ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: