Question

show that y = (2/3)e^x + e^(-2x) is a solution of the differential equation y' +2y = 2e^x

Answer 1

I'm stuck because I can't get x and dx; and y and dy together by division and multiplication.

Answer 2

Do you know how to differentiate y w.r.t. x ?

Answer 3

\[\frac{d}{dx}(y)=\frac{d}{dx}(\frac{2}{3}e^{x}+e^{-2x}) \\ \frac{dy}{dx}=\frac{d}{dx}\frac{2}{3}e^x+\frac{d}{dx}e^{-2x}\]

Answer 4

can you find the derivative of (2e^x/3)
and e^(-2x)?

Answer 5

yes

Answer 6

ok then when you are done finding y' there
...
plug it into
y'+2y

Answer 7

and you want to see if y'+2y will simplify to 2e^x

Answer 8

@yoonlim19 are you still having problems on this question?

Answer 9

I GOT IT :D Thak you :)

Answer 10

np

Answer 11

I will just say that I like your notations:)