Find the general solution of http://homework.math.ucsb.edu/webwor...ea6562ac51.png, where y is a function of t.

Could someone help me out with this? I'm not sure how to go about solving for the general solution. All I've got is .

Thanks!

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- Apr 11th 2010, 04:33 PMcdlegendaryGeneral Solution of DE
Find the general solution of http://homework.math.ucsb.edu/webwor...ea6562ac51.png, where y is a function of t.

Could someone help me out with this? I'm not sure how to go about solving for the general solution. All I've got is .

Thanks! - Apr 11th 2010, 04:38 PMdwsmith
It is a linear non-homogeneous equation.

Solve for the integrating factor. - Apr 11th 2010, 04:45 PMMath Major
Let . This will be our integrating factor.

Multiplying through to the whole equation we get that

You can work it from here. - Apr 11th 2010, 05:05 PMKrizalid
- Apr 11th 2010, 07:26 PMcdlegendary
alright so this is what I ended up trying, but I don't think it's correct. any pointers on where I went wrong?

- Apr 11th 2010, 11:13 PMderagon999
Dy/dt=1-2y

dy/(1-2y)=1 dt

integrate both sides

You should be able to get it from here - Apr 11th 2010, 11:31 PMharish21
- Apr 12th 2010, 10:46 AMcdlegendary
- Apr 12th 2010, 06:15 PMharish21
- Apr 15th 2010, 12:43 AMmoiz
y' +2y =1

first find the characteristic roots

y'+2y=0

lambda=l

l^2+2=0

l=-2

l=+-sqrt(2)i

y=e^sqrt(2)i+e^-sqrt(2)i

expand with eulers formula get sin and cosine = yg, then

find particular solution

y=A

y'=0

plug into the question

2A=1

A=1/2

Now yp=1/2

y=yg+yp

Cheers;)