Pls help! tomorrow i have EXAM! help in homework! :(

May 2010
3
0
hello

could you pls write for me ONLY general and particular solution of these Second order Inhomogeneous solutions? i know that SOLUTION for Second order Inhomogeneous is PARTICULAR solution + GENERAL solution.

Here they are (this is image because i took PRINT SCREEN)



Uploaded with ImageShack.us

Thank You! :)
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
hello

could you pls write for me ONLY general and particular solution of these Second order Inhomogeneous solutions? i know that SOLUTION for Second order Inhomogeneous is PARTICULAR solution + GENERAL solution.

Here they are (this is image because i took PRINT SCREEN)



Uploaded with ImageShack.us

Thank You! :)
Pick a problem because I am not doing them all.
 
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May 2010
3
0
could you please do this one?

Click on the image to ZOOM in



I dont want whole answer, i neew only PARTICULAR solution for this.

THANK YOU
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
could you please do this one?

Click on the image to ZOOM in



I dont want whole answer, i neew only PARTICULAR solution for this.

THANK YOU
Have you solved the complementary solution first, \(\displaystyle 2\frac{d^2x}{dt^2}-2\frac{dx}{dt}+5x=0\)?

To solve the particular solution, we need to know what annihilates \(\displaystyle e^{-2t}(2sin(2t)+3cos(t))\); therefore, what annihilates that expression?
 
May 2010
3
0
i got roots of 2k^2-2k+5=0

roots are: k1=0.5+3/2i k2=0.5-3/2i

General Solution is: e^0.5t(C1cos3/2t+C2sin3/2t)

Particular solution is: e^-2t(Asin2t+Bcost)

is it correct? :(
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
i got roots of 2k^2-2k+5=0

roots are: k1=0.5+3/2i k2=0.5-3/2i

General Solution is: e^0.5t(C1cos3/2t+C2sin3/2t)

Particular solution is: e^-2t(Asin2t+Bcost)

is it correct? :(
I tend to use the annihilator method.

\(\displaystyle e^{-2t}(2sin(2t)+3cos(t))\) is annihilate by \(\displaystyle (D^2+2)(D+1)\) or \(\displaystyle (D+2)^2+1\). You are going to have to check it since I loaned out my DE book.