a level maths, rates of change, differentiation, year 2

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a_level185
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https://prnt.sc/ugnkun

question B please
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davros
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(Original post by a_level185)
https://prnt.sc/ugnkun

question B please
What have you tried so far?

What techniques do you know for solving 1st order DEs?
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a_level185
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(Original post by davros)
What have you tried so far?

What techniques do you know for solving 1st order DEs?
I’ve done all of part a. I haven’t studied A2 integration yet. This is part of a differentiation topic.

I know all of them. Chain rule, quotient rule, product rule. I know I have to integrate for part b though. But I don’t know how to separate the fraction . I did a^(3/2) * t^(-2) . But can I simply divide both sides by a^(3/2). Is there an invisible 1 on the left so I get 1/a^(-3/2) ?
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mqb2766
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Yes it's
Int A^(-3/2) dA = Int t^(-2) dt
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a_level185
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(Original post by mqb2766)
Yes it's
Int A^(-3/2) dA = Int t^(-2) dt
Ahh, I’m finding it hard to see how you got that.

I thought if you integrate using ln x rule then it’s a(3/2)ln (t^2) all divided by 2t
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mqb2766
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(Original post by a_level185)
Ahh, I’m finding it hard to see how you got that.

I thought if you integrate using ln x rule then it’s a(3/2)ln (t^2) all divided by 2t
Separation of variables. Divide both sides by A^(3/2) then integrate wrt t. The integral on the left becomes wrt dA as dA/dt dt becomes just dA.
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a_level185
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(Original post by mqb2766)
Separation of variables. Divide both sides by A^(3/2) then integrate wrt t. The integral on the left becomes wrt dA as dA/dt dt becomes just dA.
Ive just realised I’m confused because I am learning differentiation connected change of rates. Part b was off topic and differential equations (integration). So essentially I’m trying to attempt a question on something I’ve not yet learnt. I’ll learn it and have another go. Thanks for your help
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