Question

Solve the differential equation. Find the particular solution that goes through the point (0,4).
dy/dx = (x)/(x^2 -9)

Answer 1

\[\int\limits_{}^{}dy=\int\limits_{}^{}\frac{ x }{ x^2-9 }*dx\]

Answer 2

let x^2-9=t
2x*dx=dt
x*dx=dt/2

Answer 3

\[y=\int\limits_{}^{}\frac{ dt }{ 2t }\]

Answer 4

so do u sub???

Answer 5

yeah substitution

Answer 6

+ c will also be their

Answer 7

\[y=\int\limits_{}^{}\frac{ dt }{ 2*t } +c\]

Answer 8

take the integral and then substitute for u??

Answer 9

right?

Answer 10

@gorv

Answer 11

yeah right

Answer 12

@gorv i forgot to add c loll

Answer 13

so du^2 /4u +c?

Answer 14

@g17

Answer 15

how u got it loll???
tell me

Answer 16

wait what? when you take the integral of du/2u its du^2/4u +c or no??/

Answer 17

@gorv when you take the integral of du/2u its du^2/4u +c or no??/

Answer 18

\[\int\limits_{}^{}\frac{ du }{ 2u }+c=\frac{ 1 }{ 2 }*\int\limits_{}^{}\frac{ du }{ u }+c=\frac{ 1 }{ 2 }*Ln(u)+c\]

Answer 19

would the Ln be in absolute value since u could be positive or negative @g17

Answer 20

how u got du^2...can u tell me

Answer 21

ln is natural log

Answer 22

so take positive value

Answer 23

@pnp97

Answer 24

i know ln is natural log but when it can be negative dont u put it in absolute value
and umm idk i was taking an integral but i forgot that you could take out the 1/2

Answer 25

oh ok so it has to be positive

Answer 26

so now you plug in x

Answer 27

x^2 -9 for u @g17

Answer 28

yeah right

Answer 29

and then is it 4= 1/2 ln(0^2 -9) +c?

Answer 30

@g17

Answer 31

yeah take absolute or positive value

Answer 32

as negative value is not allowed in log

Answer 33

so ln absv(0^2- 9)?

Answer 34

@g17

Answer 35

yeah u r right

Answer 36

do you solve for c now? @g17

Answer 37

yeah and out value of c in equation
that will be your particular solution

Answer 38

@pnp97

Answer 39

ohh ok! so 4= 1/2ln absv(-9) +c
@g17 how do you further simplify it?

Answer 40

c=4-1/2 ln9
y=1/2lnu+4-1/2ln9
y=1/2(lnu-ln9)+4
y=1/2ln(u/9)+4
that's it

Answer 41

thanks so much!:-) @g17