Question

what are the formulas for exponential problems? also for integrals with exponential problems

Answer 1

Also for like the problems used in linear (leibnitz) equations the e power something

Answer 2

by taking logs usualy
@ganeshie8 would be able to tell u in detail

Answer 3

alright thanks for the suggestion!

Answer 4

do u have any example problem ?

Answer 5

yes! one second

Answer 6

its from linear (leibnitz) equations. the problem was (x+1) dy/dx - y = e^3x (x+1)^2 and i got the P=-(1/1+x) and the Q=e^3x (x+1)

Answer 7

Yes, you want to find the integrating factor and multiply both sides ?

Answer 8

yes!

Answer 9

\[ (x+1) y' - y = e^3x (x+1)^2 \]

\[ y'+ \left(-\dfrac{1}{x+1}\right) y = e^3x (x+1) \]

Answer 10

no wait! its e power 3x

Answer 11

\[ (x+1) y' - y = e^{3x} (x+1)^2 \]

\[ y'+ \left(-\dfrac{1}{x+1}\right) y = e^{3x} (x+1) \]

Answer 12

IF = \(\large e^{\int -\dfrac{1}{x+1}dx} = ? \)

Answer 13

ya! i got till here but then i don't know the formulas or how to solve it from here....

Answer 14

Alright, are you fine with below also ?


IF = \(\large e^{\int -\frac{1}{x+1}dx} = e^{-\int \frac{1}{x+1}dx} = e^{- \ln |x+1|} = \dfrac{1}{x+1} \)

Answer 15

i don't really know the basics, but i get the gist of it. i got till e power - integral 1/x+1 dx but then i didn't know the formulas...do you know the formulas or have a formula sheet of some sort online?

Answer 16

I see.... there are only two formulas you need to know

Answer 17

\[\large \int \frac{1}{x} dx = \ln |x| + C\]

\[\large \int e^x dx = e^x + C\]

Answer 18

e^x is the most easy function for integrating/differentiating - as the integral or derivative of e^x is e^x itself !

Answer 19

you familiar with chain rule, eh ?

Answer 20

not really...

Answer 21

Okay, there is a recommended order for doing differential equations

Answer 22

1) solve y' = f(x) by integrating
2) separable equations
`3) linear equations`

Answer 23

Before doing linear equations, we should solve one/two equations of first two types ^

Answer 24

do have an example of the first two types of questions you mentioned?

Answer 25

yeah sure :) Before doing first two types, we should know how to integrate using substitution method. let me give u one example integral :


\[\large \int e^{ax+b} ~dx = ?\]

Answer 26

ax+b. is that right?

Answer 27

yes

Answer 28

go thru this cool short video once :
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/u_substitution/v/u-substitution

Answer 29

yay! now what?

Answer 30

hey no, sorry ax+b is not the answer

Answer 31

i have to leave now, but i'll come back online later, will you come back online here to help me again?

Answer 32

\[\large \int e^{ax+b} ~dx = a e^{ax+b} + C\]

Answer 33

Sure... I'll be around mostly :)

Answer 34

how about like in 4 hours? will you be here?