User:Egm4313.s12.team8.lucas/R2.1

=R2.1=

Problem Statement
Part i) Find the non-homogeneous L2-ODE-CC in standard form and the solution for the ODE in terms of the initial conditions ($$\displaystyle y(0)=1$$,  $$\displaystyle y'(0)=0$$) and the general excitation where $$\displaystyle r(x)=0$$, and plot the solution.

Part ii) Generate 3 non-standard, non-homoegeneous L2-ODE-CC that yield the same two roots of the characteristic equation as in Part i.

Part i
The standard form of a standard non-homogeneous L2-ODE-CC is: $$\displaystyle y''+ay'+by=r(x)$$

First, we use the given lambas to find the characteristic equation for the homogeneous solution:

Since,

then,

So,

The answer will be in the form of:

Differentiating the homogeneous solution gives:

By substituting Eqn. 1a into Eqn. 1b, we get:

Contributions
Solved and typed by: Egm4313.s12.team8.lucas 04:14, 8 February 2012 (UTC)

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