Question

(1-x^2) dy/dx - xy = 1

Answer 1

i bet this question should be answered by using linear, somehow, I get stuck on halfway.

Answer 2

yup it is linear differential eqn
did u find integrating factor? If yes then what did u get?

Answer 3

i did it, somehow, this is where i stuck, wait, need to draw it first @.@

Answer 4

i guess write it would be better

so, 1stly, i divide whole eqn with (1-x^2)

Answer 5

I.F. = exp{∫ -x/(1-x^2) dx }
put 1-x^2 = t
-2xdx= dt
after plugging the values i m getting sqrt(t) or sqrt (1-x^2)

Answer 6

turn out like this
dy/dx - (xy/1-x^2) = 1/(1-x^2)

then, my
p(x)=(-x/1-x^2)
q(x)=1/(1-x^2)

then, I integrated p(x) and ended up
/p(x)=
...

Answer 7

oh, i need to subtitute it ? D:

Answer 8

yeah, that's what i got before, then, that's the part where i stuck

Answer 9

i multiply the whole eqn with surd(1-x^2)

Answer 10

but im not sure if im in the right path or not, so, it's right isn't ?

Answer 11

if that's correct, i shall proceed with next step :D

Answer 12

yah u r going right
u need to multiply the I.F on both sides of the equation

Answer 13

and this is what i got

Answer 14

\[y \sqrt{1-x^{2}}=\int\limits_{?}^{?}(1/(1-x^{2}))\]

Answer 15

so, am i in the right track ?

Answer 16

LHS u r right
but in RHS u will get ∫ 1/ sqrt (1-x^2) dx

Answer 17

ehh, wait, i forgot to multiply it with sqrt (1-x^2)
but as far as i know, my RHS suppose to be
q(x) times I.F right ?
so, isn't it will turn out like this :-

q(x) = 1/(1-x^2)
I.F = sqrt (1-x^2)

so,
RHS = sqrt (1-x^2)/(1-x^2)

Answer 18

yup u r proceeding in the right direction

Answer 19

oh, oke, i'll proceed :D

Answer 20

but ...
lol, im kinda stuck over here
lets say that i subtitute t=1-x^2
so i have my
RHS = (t^1/2)/t
RHS = t^(1/2 - 1)
RHS = t^(-1/2)

am I right ? :D

Answer 21

so, i've to replace it back and turn to
RHS = 1/squareroot(1-x^2)

Answer 22

y r u doing substitution
it's a direct formula
∫ 1/ sqrt(1-x^2) dx = sin(x)

Answer 23

O.o
i forgot bout its existence

Answer 24

soo, this is where I wrong, haha, finally got the solution, thanks a lot ! :D

Answer 25

cool :-D

Answer 26

btw, how did u type "∫" ? *sry, im pretty new here*