Question

solve the differential equation-
[4e^(-y)*sinx-1)dx-dy=0

Answer 1

[4(e^-y)*sinx-1)dx=dy

Answer 2

dy/dx=[4(e^-y)*sinx-1]

Answer 3

after dat how should i seperate?

Answer 4

d(x+y)/dx = e^(-y)sin(x)
let x+y=z, y=z-x

Answer 5

frm where does(x+y) comes?

Answer 6

ok u took 1 to the other side

Answer 7

yes

Answer 8

use separation of variables after that

Answer 9

ok m trying it out

Answer 10

and cant we solve it by bernoullis eqn?

Answer 11

IDK ... haven't tried. my guess is no

Answer 12

m not able to solve it by ur method! :/

Answer 13

d(x+y)/dx = e^(-y)sin(x)
=> dz/dx = e^(x-z) sin(x)
=> e^z dz = e^x sin(x) dx
finish him off

Answer 14

could u plsz show me the steps so dat i could recognize my mistake

Answer 15

and 4 is missing!!

Answer 16

ohhhh!!!! ok m solving it

Answer 17

can u plz tell me the integration of e^x8cos x?

Answer 18

should i take cos x as u and e^x as v?

Answer 19

there are 3 ways of integrating it
Integrating by parts
changing sin(x) = e^(ix) and taking Imaginary values
or use symmetricity
http://www.wolframalpha.com/input/?i=Integrate%5BSin%5Bx%5D+E%5Ex%2C+x%5D

Answer 20

pls tell me u*v metho0d

Answer 21

\[
\frac{d}{dx} (e^{x} \sin(x)) = e^x \sin (x)+e^x \cos (x) \\
\frac{d}{dx} (e^{x} \cos(x)) = e^x \cos (x)-e^x \sin (x)
\]
subtract second from first .. and integrate on both sides

Answer 22

its not gettin cancelled

Answer 23

the left side is
\[ \frac{d}{dx} (e^x\sin(x) - e^x \cos(x)) = 2 e^x \sin(x)\]

integrate both sides and get your result.

Answer 24

\[ \frac 1 2\int \frac{d}{dx} (e^x\sin(x) - e^x \cos(x)) dx = \int e^x \sin(x)dx\]

Answer 25

http://www.wolframalpha.com/input/?i=Integrate%5BSin%5Bx%5D+E%5Ex%2C+x%5D

Answer 26

ok thanku for ur help!

Answer 27

you are welcome