Question

Find a particular solution of
y′′−3y−4y=3e2t

Answer 1

You can make a "guess" at a solution here , what would you say the form of y= ?

Answer 2

A hint is \[y=Ae ^{?t}\]

Answer 3

yes. please continue

Answer 4

I'm not going to do the work for you.

Answer 5

please, teach me

Answer 6

i know that that is the particular intigral

Answer 7

y'=2Ae^2t

Answer 8

You see on the right hand side you have \[3e ^{2t}\] , so your solution will have the form \[y=Ae ^{2t}\]

Answer 9

and y''=4Ae^2t

Answer 10

Correct. Now plugging into the equation, you solve for A, and your particular solution is found.

Answer 11

ok

Answer 12

thanks ,now i understand

Answer 13

No problem :)