Question

What do you get for the following first-order linear differential equation?
http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36/MATA36-IMG-004.png

Answer 1

Does y' represent dy/dx ?

Answer 2

Yes

Answer 3

This is not seperable for sure

Answer 4

@mahmit2012
@Mertsj
@myininaya
@dpaInc

Answer 5

multiply both sides by \(e^{3x}\)
you get
\[e^{3x}\frac{dy}{dx}+3ye^{3x}=5e^{3x} \sin e^{3x}\]\[\frac{d(e^{3x}y)}{dx}=5e^{3x}\sin e^{3x}\]\[d(e^{3x}y)=(5e^{3x}\sin e^{3x})dx\]Integrate both sides you will get your result!

Answer 6

I did that. My problem is somewhere with the integration I guess...

Answer 7

How about you do the integration and tell me what you get. I already did my attempt. I want to see how your and my answer differ.

Answer 8

ok. give me a min.

Answer 9

formula
http://www.wolframalpha.com/input/?i=integrate+e^%28ax%29+cos+bx

Answer 10

wolf shows something different. http://www.wolframalpha.com/input/?i=integrate+5e%5E%283x%29+sin+%28e%5E%283x%29%29

Answer 11

e^3x was inside sin ... oh ... that's even easier,, just use simple substitution

Answer 12

yep! but the required answer is lot different. i guess..
@QRAwarrior is that the answer , in the link you posted along with your question?

Answer 13

experimentX, I would like to know if you could compare your answer to mine (I have link posted in first post_)

Answer 14

Yes

Answer 15

That was my answer, and that was wrong.

Answer 16

answer in that link you posted seems wrong!

Answer 17

Yes but why?

Answer 18

for the sake of ease, i trust wolf
http://www.wolframalpha.com/input/?i=y%27+%2B+3y+%3D+sin%28e%5E%283x%29%29

Answer 19

\[ \int 5e^{3x}\sin e^{3x} dx= \frac 5 3 \int \sin u du = - \frac 5 3 \cos u \]
were u = e^3x

Answer 20

this part you got wrong

Answer 21

really?

Answer 22

Wow! I thought I had to do integration by parts for that

Answer 23

I think that might be it.

Answer 24

Wait nevermind, how?