verify that the given function satisfies both the differential equation and the initial condition.
y'+3y=e^-t y(0)=-1/2 y=((e^-t)/2)-e^(-3t)

Question

verify that the given function satisfies both the differential equation and the initial condition. 
y'+3y=e^-t      y(0)=-1/2    y=((e^-t)/2)-e^(-3t)

tkhunny · Answer

You should NEVER stumble over a "verify".  Just do it.

You have y.
Find y'.
Check it out.

mony01 · Answer

I don't know how to do the derivative of y

tkhunny · Answer

Find these derivatives:

$y = e^{t}$

$y = e^{-t}$

$y = ½e^{-t}$

$y = e^{-3t}$

Please demonstrate proficiency.

mony01 · Answer

is the derivative for y=e^t is y'=e^t
y=e^-t is y'=-e^-t
y=e^-3t is y'=-3e^-3t

tkhunny · Answer

The third one seems to be missing.

mony01 · Answer

i cannot see what you wrote is it the same as y=e^-t

tkhunny · Answer

Oh, right.  Silly coding issues.  $y = \dfrac{1}{2}e^{-t}$

mony01 · Answer

$$y'=-\frac{ e ^{-t} }{ 2 }$$

tkhunny · Answer

That's the spirit.

Guess what?  There is now nothing in your way that can prevent you from finding that derivative in the original problem statement.

mony01 · Answer

is it $$y'=-\frac{ e ^{-t} }{ 2}+3e ^{-3t}$$

tkhunny · Answer

There it is!  Okay, substitute and go!

mony01 · Answer

what do i do with the y(0)?