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Unformatted text preview: A170 Appendix A Ordinary Diﬀerential Equations: Review of Concepts and Methods Using to solve ODE Let us start with the simplest command that you can use to solve an ode. It is the DSolve command. We illustrate by
examples the different applications of this command. The simplest case is to solve y' = y
DSolve y ’ x
yx x y x ,y x ,x C1 The answer is y= C ex as you expect. Note how Mathematica denoted the constant by C[1]. The enxt example is a 2nd
order ode
DSolve y ’’ x
yx x y x ,y x ,x
x C1 C2 Here we need two arbitrary constants C[1] and C[2]. Let's do an intial value problem. Solving an Initial Value Problem
Here is how you would solve y'' = y, y(0)=0, y'(0)= 1
DSolve
yx y ’’ x
1
2 x y x ,y 0
1 0, y ’ 0 1 , y x ,x 2x As you see, the initial value problem has a unique solution (there are no arbitrary constants in the answer. ...
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.
 Fall '11
 StuartChalk

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