Question

First order DE question, won't solve correctly for me http://i.imgur.com/BC2ZP.jpg

Answer 1

v=x/t so t=x/v

Answer 2

Subbed this back into the original equation, it's not working out

Answer 3

(x/v)^2(t*dv/dt+v)=vt(t+z)

Answer 4

I should mention I got the derivative of x using the product rule.

Answer 5

as x=vt

Answer 6

I've tried a question similiar using help from openstudy, but I can't see what I am doing wrong in this case.

Answer 7

seems like this type
http://en.wikipedia.org/wiki/Bernoulli_differential_equation

Answer 8

x=vt
x'=v't+v

\[t^2(\frac{dv}{dt}t+v)=vt(t+vt)\]\[\large{\frac{dv}{dt}t^3+vt^2=vt^2+v^2t^2}\]\[\frac{dv}{dt}t^3=v^2t^2\]now its a seperable differential equation..Can u take it from here?

Answer 9

much better than solving linear differential equation!!

Answer 10

Bingo, I have no idea how you do them so fast!!

Answer 11

lol

Answer 12

I think I should stopping immediately subbing new values back in the original equation...

Answer 13

So the integrate the following t 1/dt = v^2 1/dv

Answer 14

?

Answer 15

Sorry -v^2 dv=-t dt

Answer 16

and integrate that

Answer 17

Where did that come from?

Answer 18

Seperating t(dv/dt)=v^2

Answer 19

Multiplied across by dt.

Answer 20

seperating this u get\[\large{\frac{dv}{v^2}=\frac{dt}{t}}\]

Answer 21

Ah crap, sorry. Yeah so in the end its 1/v^2 dv = 1/t dt