where assume that and are continuous at

I don't know where to start this problem. any suggestions?

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- Oct 24th 2010, 11:37 PMquestionboyUndetermined Coefficients

where assume that and are continuous at

I don't know where to start this problem. any suggestions? - Oct 25th 2010, 03:29 AMAckbeet
Solve the DE separately in each region, without applying the conditions. Then apply the conditions to find the constants of integration.

- Oct 25th 2010, 06:48 AMHallsofIvy
Each separate solution will involve

**two**unknown constants, for a total of**four**. The boundary conditions will give two equations for those. Use the fact that the solution function must be differentiable at to find the other two- that is, the two functions and the derivatives of the two functions must be the same at . - Oct 25th 2010, 04:39 PMquestionboy
what is the final answer should like?

- Oct 25th 2010, 05:41 PMquestionboy

what should i do - Oct 25th 2010, 06:16 PMHallsofIvy
Go back and start all over again! Your characteristic equation is which does NOT have roots 1 and -3!

What are the roots of ? What are two independent solutions to ?

Now, with right hand side "1", try a solution of the form y= A, a constant. What "A" satisifies ?

Now, you should have two functions, Y1 and Y2, say, so that Y1 is correct between 0 and (I am assuming you meant " " and not as you had at first) and Y2 is correct for . Y1 will, of course, involve two unknown constants (and don't write them**both**as "c"!). You can determine those from the initial conditions y(0)= 0 and y'(0)= 0. Once you know those, you know Y1(t) completely and can evaluate it at . Y2 will also involve two unknown constants. You can determine those from and . - Oct 25th 2010, 08:18 PMquestionboy

what should i do now?

set Y1=Y2?