Question

ODE problem change of variable problem.

Answer 1

I hate these questions can see what else I can do

Answer 2

Here's my work so far.

Answer 3

are you asking (i)?

Answer 4

Yes.

Answer 5

Not a fan of these questions, you need to think outside the box a lot of the time

Answer 6

I noticed a big mistake, I currently at this point.

Answer 7

plugin to WA ...and check your answer

Answer 8

@experimentX Wolfram Alpha?

Answer 9

yep

Answer 10

I did, it gives me a separable differential equation

Answer 11

I can't figure out however how to get my RHS to look like t((z^2)+2)

Answer 12

yep ... separate the variables and integrate it.

Answer 13

can you use draw or equation feature?

Answer 14

I can use math type it's a lot fast that equation feature here.

Answer 15

I've posted my working above. but I know noticed some things are wrong. I know I am close to working this out my RHS is slightly different to what the question wants.

Answer 16

It's x=zt though

Answer 17

dz/dt*t+z

Answer 18

I've made a mess of this now...

Answer 19

I'm currently at

Answer 20

\[tx\frac{\text dx}{\text dt}=2t^4+t^2x^2+x^2\]
\[\frac{\text dx}{\text dt}=\frac{2t^3}x+tx+\frac xt\]

\[z(t)=\frac{x(t)}t\]\[x(t)=zt\]\[\frac{\text d (x(t))}{\text dt}=z't+z\]
\[\frac{\text d(z't)}{\text dt}+z=\frac{2t^2}z+zt^2+z\]

Answer 21

ops my last line is wrong

Answer 22

\[\frac{\text dz}{\text dt}t+z=\frac{2t^2}z+zt^2+z\]

Answer 23

now minus the z and divide by t

Answer 24

\[\frac{\text dz}{\text dt}=\frac{2t}z+zt=t\left(\frac 1z+z\right)\]
which is seperable

Answer 25

ops 1=2

Answer 26

I have to get the answer in the form the question asks though

Answer 27

all you have to is multiply by z

Answer 28

and fix the 1=2 error i made

Answer 29

I don't see a mistake...it's look fine once I multiply be z and factorise the RHS.

Answer 30

cool