Question

Change of variable ODE question

Answer 1

Hate these question, cannot do them at all. More of a puzzle more than anything. Here's my attempt.

Answer 2

@amistre64 any ideas?

Answer 3

looks ok, as far as you went. but if v= x/t then x= vt
sub in vt for all the x's

Answer 4

@phi

Answer 5

I have no idea what else I can do now.

Answer 6

I would collect terms. I would divide out common terms.

Answer 7

What do you mean, they only extra thing I can do is \[t ^{2}v ^{3}t ^{3}=t ^{5}v ^{3}\]

Answer 8

That I can see anyway!

Answer 9

what about (vt)^4 on both sides of the equation?
and there is t^4 in all the terms. multiply both sides by t^(-4)

Answer 10

ok dividing by t^4, will cancel with the LHS and get a +1 on the right.

Answer 11

I'm at this point now.

Answer 12

It will cancel the other t^4 on the right hand side as well.

Answer 13

you made a mistake going to the last line.

you can multiply both sides of the equation by t^(-4)
that means multiply every term by t^-4

Answer 14

or another way to think of it
factor out t^4 from each side so you get
t^4( v^3 t dv/dt+v^4)= t^4(v^4+1)

now multiply both sides by t^-4

Answer 15

Like this??

Answer 16

2nd term on the left side looks wrong. you start with v^4 t^4 and multiply by t^(-4):
t^(-4) * v^4 * t^4

Answer 17

@phi Sorry, I suck at this.

Answer 18

Dividing the whole equation by t^4

Answer 19

now subtract v^4 from both sides

Answer 20

remember, you know what the answer is, as given in the problem. so you want
t dv/dt on the left.

Answer 21

Almost!

Answer 22

close. the second to last line is good.

if you had 2x-x what do you get
do the same for 2v^4 - v^4

the other major point:
v^3 does not divide into the 1 up top. so you cannot simplify any further

Answer 23

THANK YOU!!

Answer 24

I hate this question so much, it's not test of calculus at all. It's just a puzzle more than anything

Answer 25

it is algebra, and you have to know algebra before calculus.
I would learn a few rules of algebra, and then it won't be a puzzle, just methodical work.

Answer 26

True, I just need to be careful what I am canceling out as well.

Answer 27

the problem is you seem to know a lot, but are missing some simple ideas, so it's tough to start at the beginning to fill in the missing blanks, because most of it might be too boring.

but based on this question, I would recommend knowing how to combine like terms

a^2b^3 + 3a^2b^3 =4 a^2 b^3
of course a^2 b^2 + 3 a^2 b^3 cannot be combined.
(different powers for b)

Answer 28

can I try ?

Answer 29

Fire ahead, mahmit. You solve equations in record time.