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# applying differential equations to real-life problems watch

1. Hi guys ,
I'm practising differential equations where you need to integrate both sides to find the general solution as it's shown in the attachment I'm a bit confused of integrating -k dt which which gives out -kt can anyone help?thanks
Attached Images

2. (Original post by Alen.m)
Hi guys ,
I'm practising differential equations where you need to integrate both sides to find the general solution as it's shown in the attachment I'm a bit confused of integrating -k dt which which gives out -kt can anyone help?thanks
is a constant, i.e: nothing but a number. How would you integrate ? You'd get , I hope?

So:
3. (Original post by Zacken)
is a constant, i.e: nothing but a number. How would you integrate ? You'd get , I hope?

So:
Thanks man
4. (Original post by Alen.m)
Thanks man
No problem.
5. (Original post by Zacken)
No problem.
On the topic of DE's, do you know if i'm allowed to integrate between limits rather than using +c in c4 (e.g. integrate between p0 and P), which is mathematically valid but i don't think it is normally in mark schemes
6. (Original post by samb1234)
On the topic of DE's, do you know if i'm allowed to integrate between limits rather than using +c in c4 (e.g. integrate between p0 and P), which is mathematically valid but i don't think it is normally in mark schemes
You are. No problem about it.
7. (Original post by Zacken)
You are. No problem about it.
thanks, i hate using +c lol
8. (Original post by Zacken)
You are. No problem about it.
Can i just also ask you one single question about e equations in the attachment, im abit confused and also couldnt find anything usefull on my note about how 1/a is written as A
9. (Original post by Alen.m)
Can i just also ask you one single question about e equations in the attachment, im abit confused and also couldnt find anything usefull on my note about how 1/a is written as A
is an arbitrary constant. That is, it can be any number. It doesn't matter what form I like it in.

For example, if I was doing , I could write the in whichever way I want. I could use or or , it doesn't matter and nobody cares because it'll all work out in the end.

So, in cases like this. you could leave your answer as but we choose to say and write because it just looks nicer.
10. (Original post by Zacken)
is an arbitrary constant. That is, it can be any number. It doesn't matter what form I like it in.

For example, if I was doing , I could write the in whichever way I want. I could use or or , it doesn't matter and nobody cares because it'll all work out in the end.

So, in cases like this. you could leave your answer as but we choose to say and write because it just looks nicer.
All clear now, for the other part i was trying to sketch the graph of y=30000-20000e^0.2In0.9t and saw this bullet point from the text book saying that remmeber that0.2In0.9t is negative , can you please touch on that a little bit so i underestand what the text book meant by that thanks
11. (Original post by Alen.m)
All clear now, for the other part i was trying to sketch the graph of y=30000-20000e^0.2In0.9t and saw this bullet point from the text book saying that remmeber that0.2In0.9t is negative , can you please touch on that a little bit so i underestand what the text book meant by that thanks
Are you meant to sketch the graph in some interval? Because that's quite wrong. for example.
12. (Original post by Zacken)
Are you meant to sketch the graph in some interval? Because that's quite wrong. for example.
Well actually it's part c of the question in the attachment , i've managed to do the rest of it but kind of confused by the given hint by text book on part c. I can send you all answers as attachemnets if you want so you dont go through all of them
13. (Original post by Alen.m)
Well actually it's part c of the question in the attachment , i've managed to do the rest of it but kind of confused by the given hint by text book on part c. I can send you all answers as attachemnets if you want so you dont go through all of them
I think the textbook is wrong, tbh. But really, all you need to know is that is always positive, so you're always doing so the graph nears the line as increases.
14. (Original post by Zacken)
I think the textbook is wrong, tbh. But really, all you need to know is that is always positive, so you're always doing so the graph nears the line as increases.
It's been couple of times that its answer makes me confus and lost tbh but as you said all i need to do is to find the 10000 value on c graph first and the line nears 30000 as t increases
15. (Original post by Alen.m)
It's been couple of times that its answer makes me confus and lost tbh but as you said all i need to is to find the 10000 value on c graph first and the line nears 30000 as t increases
Yep, pretty much.
16. (Original post by Zacken)
Yep, pretty much.
Actually the graph suggests that c gets bigger and bigger as it approaches 30000 and as t increases isn't?
17. (Original post by Alen.m)
Actually the graph suggests that c gets bigger and bigger as it approaches 30000 and as t increases isn't?
Ah, fuark! Ignore me. I thought the equation was instead of , So what we have is approximately, so as t gets bigger, gets smaller and smaller, so the graph approaches . My apologies.
18. (Original post by Zacken)
Ah, fuark! Ignore me. I thought the equation was instead of , So what we have is approximately, so as t gets bigger, gets smaller and smaller, so the graph approaches . My apologies.
But c on the graph is increasing as the graph suggests isn't? Is it because it's been muliplied by 20000?
19. (Original post by Alen.m)
But c on the graph is increasing as the graph suggests isn't? Is it because it's been muliplied by 20000?
It's because you're doing 30,000 - something that gets smaller and smaller. So as you start out, it's quite big and 30,000 - big number = small number. But then as t gets bigger, e^(-0.02t) gets smaller so you do 30,000 - smaller number = bigger number. And hence the graph is increasing. But then, at a certain point, when t gets really big e^(-0.02t) is almost 0 so 30,000 - almost 0 is almost 30,000, etc...? You get me?
20. (Original post by Zacken)
It's because you're doing 30,000 - something that gets smaller and smaller. So as you start out, it's quite big and 30,000 - big number = small number. But then as t gets bigger, e^(-0.02t) gets smaller so you do 30,000 - smaller number = bigger number. And hence the graph is increasing. But then, at a certain point, when t gets really big e^(-0.02t) is almost 0 so 30,000 - almost 0 is almost 30,000, etc...? You get me?
So basically it's a graph of y=30000-20000e^0.2tIn(0.9)? The reason im asking is because the text book stated it's a graph of e^0.2In(0.9t) which should definetely be different Attachment 511585511587
Attached Images

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