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# FP2 Differential equations Help watch

1. Find the solution to the differential equation (4-x^2)^1/2 dy/dx = (4-y^2) ^1/2 for which y= -1 and x=1.

I just don't know how to integrate (4-y^2)^1/2 = (4-y^2)^1/2

2. (Original post by ChemBoy1)
Find the solution to the differential equation (4-x^2)^1/2 dy/dx = (4-y^2) ^1/2 for which y= -1 and x=1.

I just don't know how to integrate (4-y^2)^1/2 = (4-y^2)^1/2

Not sure what the second line means.

Use the substitution x=2sinu.
3. (Original post by ChemBoy1)
Find the solution to the differential equation (4-x^2)^1/2 dy/dx = (4-y^2) ^1/2 for which y= -1 and x=1.

I just don't know how to integrate (4-y^2)^1/2 = (4-y^2)^1/2

Then just use two subs:

4. Update: I managed to get the equation as arcsin y/2 = arcsin x/2 +c. The question asks to express my answer in a form not involving trig functions. I don't see how I can do that.

Thanks
5. (Original post by ChemBoy1)
Update: I managed to get the equation as arcsin y/2 = arcsin x/2 +c. The question asks to express my answer in a form not involving trig functions. I don't see how I can do that.

Thanks
First of all, determine what is.

Then, write and then apply the compound angle formula on the RHS.
6. I got c as pi/3. Ho do I convert it to an expression not involving trig functions?
(Original post by RDKGames)
First of all, determine what is.

Then, write and then apply the compound angle formula on the RHS.
7. (Original post by ChemBoy1)
I got c as pi/3. Ho do I convert it to an expression not involving trig functions?
8. Sorry just saw that thanks. How can you use compound angle formula because i still got Sin (Sin-1 x) etc.
(Original post by RDKGames)
9. (Original post by ChemBoy1)
Sorry just saw that thanks. How can you use compound angle formula because i still got Sin (Sin-1 x) etc.
(obviously) so, we just need . If we denote then we have and we can use a right-angled triangle to determine what is.

EDIT: Or just use for this part.
10. Still confused with the right angle triangle thing. becuase the hyp = 2 and the opp = x. The adj would just be a separate variable and that would not work? Could you please help me out?
(Original post by RDKGames)
(obviously) so, we just need . If we denote then we have and we can use a right-angled triangle to determine what is.

EDIT: Or just use for this part.
11. (Original post by ChemBoy1)
Still confused with the right angle triangle thing. becuase the hyp = 2 and the opp = x. The adj would just be a separate variable and that would not work? Could you please help me out?
The adj would just be sqrt(hyp^2-opp^2) by Pythagoras
12. The book got y= 1/2 x - 1/2x (3(4-x^2))^1/2.

I got no where near that answer, could you help elaborate.
FYI values are y= -1 and x=1
13. (Original post by ChemBoy1)
The book got y= 1/2 x - 1/2x (3(4-x^2))^1/2.

I got no where near that answer, could you help elaborate.
FYI values are y= -1 and x=1
OK, first of all, . It is in fact

Next, we have

Finish it off.
14. Nearly got it, except for how they got 3(4-x^2)^1/2
(Original post by RDKGames)
OK, first of all, . It is in fact

Next, we have

Finish it off.
15. (Original post by ChemBoy1)
Nearly got it, except for how they got 3(4-x^2)^1/2
Factor out 1/4 inside the root, then bring that factor outside the root. Similarly, merge root(3) with the main root since
16. Thank you so much! You have helped a lot! Sorry if I have sounded very silly to you.
(Original post by RDKGames)
Factor out 1/4 inside the root, then bring that factor outside the root. Similarly, merge root(3) with the main root since
17. (Original post by ChemBoy1)
Thank you so much! You have helped a lot! Sorry if I have sounded very silly to you.

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