Question

First order linear differential equation! Help!

Answer 1

\[\frac{ dy }{ dx}=(x ^{2}-1)y ^{2} , y(0)=1\]

Answer 2

Is this right?
\[\int\limits_{}^{}\frac{ 1 }{ y ^{2} }dy=\int\limits_{}^{}(x ^{2}-1)dx\]

Answer 3

\[-\frac{ 1 }{ y }=\frac{ 1 }{ 3 }x ^{3}-x+C\]

Answer 4

If that's right, then that's where I'm stuck :P

Answer 5

where do you have to get? do you just have to set it equal to y?

Answer 6

Yup!

Answer 7

Then find C, and find the particular solution

Answer 8

Btw, is it just my computer or isn't any of the smartscores showing?

Answer 9

I can see your score

Answer 10

I would just plug in 0,1 and solve for C

Answer 11

Hm, it just seems too easy, if you get me :P

Answer 12

It does but I think that is what you do. You already did the "hard" part

Answer 13

But wouldn't it be "correct" to first find the expression for y?

Answer 14

Hmh, I see now that I get the same answer any way, so I guess not :P

Answer 15

either way you will get the same C. so you can do either first. I think it is easier to find C now and then solve for y but what ever is better for you

Answer 16

Ok, thanks!^^