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# First Order Differential Equations Questions

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1. First Order Differential Equations Questions
So I've been having some trouble with a couple of differential equations.

1) sqrt(2-x^2)*(dy/dx) -x*(y+5)=0 where y>-5

I rearranged to get

(1/(y+5)) dy= x/sqrt(2-x^2) dx

Then intergrating to get

ln|y+5|=-sqrt(2-x^2) +k

then reworking to get

y=e^(-sqrt(2-x^2)) -5 +C which isn't right.

2) (dy/dx) -10 +2*x^2 +5*y^2 +(y^2)*(x^2)=0

(dy/dx) + y^2(5+x^2)= 10 -2*x^2

which is simular to standard form ((dy/dx) + f(x)*y=h(x)) but there's an extra y?
2. Re: First Order Differential Equations Questions
(Original post by salmon12345)
y=e^(-sqrt(2-x^2)) -5 +C which isn't right.
Just skimming, but why do you think it is not right?
3. Re: First Order Differential Equations Questions
(Original post by gff)
Just skimming, but why do you think it is not right?
I entered it on the system my Uni uses and it says it's incorrect. Unfortunatly it doesn't say why or give me the right answer.
4. Re: First Order Differential Equations Questions
(Original post by salmon12345)
I entered it on the system my Uni uses and it says it's incorrect. Unfortunatly it doesn't say why or give me the right answer.
Ok, fair enough. Can you look at it again, and note that if , then .

The other equation is first-order non-linear. Is by any chance the sign of positive?
5. Re: First Order Differential Equations Questions
(Original post by gff)
Ok, fair enough. Can you look at it again, and note that if , then .

The other equation is first-order non-linear. Is by any chance the sign of positive?
Thanks, I've got the first one now and I'll remember to be more careful with my C's.

And I've checked, the 10 is definitely negative.
6. Re: First Order Differential Equations Questions
(Original post by salmon12345)
And I've checked, the 10 is definitely negative.
Well, the solution to this equation is not obvious to me.

One can put it into and play with Riccati's equation.
7. Re: First Order Differential Equations Questions
(Original post by gff)
Well, the solution to this equation is not obvious to me.

One can put it into and play with Riccati's equation.
I've just looked again and it turns out the equation is actually
(dy/dx) -10 -2*x^2 +5*y^2 +(y^2)*(x^2)=0 does that make a difference? Because we definitely haven't done Riccati yet.
8. Re: First Order Differential Equations Questions
(Original post by salmon12345)
I've just looked again and it turns out the equation is actually
(dy/dx) -10 -2*x^2 +5*y^2 +(y^2)*(x^2)=0 does that make a difference? Because we definitely haven't done Riccati yet.
It does, indeed.

.

Does that help?
9. Re: First Order Differential Equations Questions
(Original post by gff)
It does, indeed.

.

Does that help?
Yep, thanks a lot.

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Last updated: April 20, 2012
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