Hey everyone, I need help understanding solving this equation as it deals with an input function that is discontinuous, which I don't know how to handle.

for

for

Solve

The two intervals:

for

and

for

with and

Can anyone help me?

Thanks

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- May 6th 2011, 06:03 AMNguyenSecond Order Nonhomogeneous Equation
Hey everyone, I need help understanding solving this equation as it deals with an input function that is discontinuous, which I don't know how to handle.

for

for

Solve

The two intervals:

for

and

for

with and

Can anyone help me?

Thanks - May 6th 2011, 06:51 AMProve It
Solve the homogeneous equation http://quicklatex.com/cache3/ql_ae3a...765eaaf_l3.png.

It has characteristic equation http://quicklatex.com/cache3/ql_1378...8f9c350_l3.png, which has solution http://quicklatex.com/cache3/ql_18f0...b29dce9_l3.png.

From this, we can determine that the solution to the homogeneous DE is http://quicklatex.com/cache3/ql_8dbf...aa5143a_l3.png. This is also the entire solution when http://quicklatex.com/cache3/ql_cf75...7b7f884_l3.png.

Now for the nonhomogeneous solution, i.e. when http://quicklatex.com/cache3/ql_07bb...bd960ba_l3.png, we try http://quicklatex.com/cache3/ql_0521...4106705_l3.png. This would mean http://quicklatex.com/cache3/ql_dbcc...cb5330d_l3.png and http://quicklatex.com/cache3/ql_5dc0...6348c2c_l3.png.

Substituting into the DE gives

http://quicklatex.com/cache3/ql_5997...721ec5d_l3.png.

http://quicklatex.com/cache3/ql_a0e5...cc26284_l3.png

So the particular solution is http://quicklatex.com/cache3/ql_ad3e...904f10c_l3.png.

Therefore when http://quicklatex.com/cache3/ql_07bb...bd960ba_l3.png, the solution of the DE is http://quicklatex.com/cache3/ql_b863...2575bd0_l3.png.

Now you will need to use your boundary conditions to evaluate A and B. - May 6th 2011, 07:15 AMbugatti79
- May 6th 2011, 07:30 AMProve It
Because g(x) = 0 when x > pi/2, which means the DE is homogeneous in that domain.

- May 6th 2011, 08:05 AMTheEmptySet
- May 6th 2011, 06:00 PMNguyen
Thanks Prove It and TheEmptySet, I did the question the same way as Prove It but crossed it out becuase I didn't know how to deal with g(x) being discontinuous.

I got y= 5/6 sin(2x) +cos(2x)+1/3 sin(x) - May 7th 2011, 06:22 AMtopsquark