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Differential equations

Right, I've got a few of these I'm stuck on:

t*(dA/dt) = (1/A) + A

I think the answer to this is t = k*e((A^2 +1) /A) or am I wrong?

Also:

r*(dθ/dr) = tan ( θ )

Annnnd finally:

U*(du/dv)= ( 1 / (v)^(0.5) ) + v^(1/3)

How do I do these/what are the actual answers so I can check my working if/when I managed to do them? Many thanks for any help :smile:

Reply 1

jobo3

Anyone? Sorry, I'm in a bit of a rush :frown:

Reply 2

Glutamic Acid

My result isn't the same as yours for the first one: rewrite the right-hand side as

\dfrac{A^2+1}{A}

and it becomes easily separable.

Spoiler

Reply 3

jobo3

Glutamic Acid

My result isn't the same as yours for the first one: rewrite the right-hand side as

\dfrac{A^2+1}{A}

and it becomes easily separable.

Spoiler

Thanks

Also, any ideas for the other 2?

Reply 4

Daniel Freedman

jobo3

Thanks

Also, any ideas for the other 2?

The second is also just separation of variables. Divide through by tan(theta) and r, and 'multiply' through by dr. Integrate both sides.

For the third, just 'multiply' through by dv and integrate both sides...