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

#### kabal

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) Thank You! #### dwsmith

MHF Hall of Honor
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) Thank You! Pick a problem because I am not doing them all.

• mr fantastic

#### dwsmith

MHF Hall of Honor
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?

#### kabal

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
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.