First Order Differential Equations Questions
Maths and statistics discussion, revision, exam and homework help.
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First Order Differential Equations QuestionsSo 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
I'm not sure about this one, I was thinking maybe
(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? -
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Re: First Order Differential Equations QuestionsJust skimming, but why do you think it is not right?(Original post by salmon12345)
y=e^(-sqrt(2-x^2)) -5 +C which isn't right. -
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Re: First Order Differential Equations QuestionsI 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.(Original post by gff)
Just skimming, but why do you think it is not right? -
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Re: First Order Differential Equations QuestionsOk, fair enough. Can you look at it again, and note that if(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.
, then 
.
The other equation is first-order non-linear. Is by any chance the sign of
positive?
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Re: First Order Differential Equations QuestionsThanks, I've got the first one now and I'll remember to be more careful with my C's.(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?
And I've checked, the 10 is definitely negative. -
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Re: First Order Differential Equations QuestionsWell, the solution to this equation is not obvious to me.(Original post by salmon12345)
And I've checked, the 10 is definitely negative.
One can put it into
and play with Riccati's equation.
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Re: First Order Differential Equations QuestionsI've just looked again and it turns out the equation is actually(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.
(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. -
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Re: First Order Differential Equations QuestionsIt does, indeed.(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.
.
Does that help?
