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Given the following equations, classify them as parabolic, hyperbolic or elliptic if applicable: If not applicable, please provide a reason Uxx + Uxy 2u = 0 Ux + ux...

Question

Given the following equations, classify them as parabolic, hyperbolic or elliptic if applicable: If not applicable, please provide a reason Uxx + Uxy 2u = 0 Ux + uxy 2u =0 ut + uxx + Ux = 1 ut + Uxx + Ux+u =1 ut + Uxx + Z(u2)x =1

Given the following equations, classify them as parabolic, hyperbolic or elliptic if applicable: If not applicable, please provide a reason Uxx + Uxy 2u = 0 Ux + uxy 2u =0 ut + uxx + Ux = 1 ut + Uxx + Ux+u =1 ut + Uxx + Z(u2)x =1



Answers

For each of the differential equations in Exercises $1-10$ find a solution which contains two arbitrary functions. In each case determine whether the equation is hyperbolic, parabolic, or elliptic. $$ 2 \frac{\partial^{2} u}{\partial x \partial y}+3 \frac{\partial^{2} u}{\partial y^{2}}=0 $$

Hello. Today we are doing this differential equation to that's where your intellect square and it's too, that's where your panda like silver plus five. That's why you opened advice particles to zero. We need to find out a solution for this explosion as well as we also need to find out mm that whether the situation is parabolic, hyperbolic or elliptic. So the quadratic equation aimed squarely lesbian plus equals to zero. For this particular equation will be to subscribe minus to a plus five equals to zero over a is to B s minus two and CS five by this. Or to take equation we find out the roots of the situation. So the roots of the situation will really find out from this formula minus three plus minus B squared minus four to save on to A. So we get our roots as M one equals 21 by two plus three. Where do I? And I am too because you want my 2 -3 to I. So these will be the two doctors. Quarterdeck equation here is not equal to zero. And the roots are testing. So this is an example of homogeneous leader equation and we have a solution from your own number 14.1 of homogeneous linear equations which is as follows U equals two. F. Vibe plus one by two plus three. But do I X plus G via plus one by two minus three by two? I X. So this is our solution. This is a solution for the situation where F and G are arbitrary functions of their respective arguments. Also from equation number one, we had a chance to do because to minus two and Sequels to fight from this, we find out B squared minus four A. C and b squared minus four. Policy comes out to be minus 36 -36 is less than zero, so if please prime minus four A C is less than zero. They suggest that the situation number one is elliptic and that's our answer. Thank you. Bye bye.

Hello. Today we are doing this question that Elsewhere you upon Alex Square -2. That's where you upon Alex tell why it goes to zero. This is a differential equation given to us and we need to find out a solution for for it as well as we also need to find out whether this equation is parabolic capability or elliptic. So the quadratic equation named scramblers Bm plus C was +20. For this equation will be and scum minus to a musical C zero. Because from the situation We find out that equals two, one Be close to -2 and Sequels to zero. So we find that roots of the situation here is not equal to zero and it has distinct roots and many close to zero. And then do it goes to two. Therefore it is a homogeneous lead to depression bitch. We'll have it solution as U equals two F. Y. Because the first route was zero plus G. Y plus two. Second road do X By Thoreau # 14.1 of Homogeneous Linear Equations. The F is an arbitrary functional Y only and G is an arbitrary function of its argument. Now. Also from equation number one we had a close to one because two minus two and Sequels to zero. This implies that the school minus four. A C will be equal to four, which is greater than zero. And if B squared minus four A C is greater than zero. This suggests that this equation number one is hyperbolic and that's a branch to thank you

Hello. Today we are doing this differential equation that That's where you open the square plus two. That's where you're gonna lick salary plus five. That's where you're born device where it goes to zero. So we need to find out a solution of the situation and also we need to find out whether the situation is parabolic, hyperbolic or olympic. So the quality equation am scrap lesbian plus equals to zero. For this particular equation Very weak and helpless to M-plus five equals to zero. Here it goes to one because to do and see close to fight. So the roots of this equation we find out the root by this formula M equals two minus B plus minus. And the road based crime and Zaporizhia point to a. So we're fine that the roots of this equation R. M. When it comes to minus mint plus two I an M two equals two minus one minus two. Y. So these are the two distinct routes here is not equal to zero and the division has distinct groups. So this is a homogeneous linear equation and by total number 14.1 of homogeneous synthetic versions. We have its solution as this. You close to F via plus minus one plus two Y. X plus G via plus minus one minus two Y. X. So this is the solution for the situation where F and G are arbitrary functions of the respective argument. Also from equation one we had a close to one week was to do and see was to fight. So by this we get b squared minus four. Easy. This is why -40s. He comes out to be -16, which is less than zero. So if P squared minus four a c is less than zero. This suggests that the situation is electric. So this is our answer. Thank you. Okay, Okay.

Hello. Today we are doing this differential equation that they'll square you upon the like square plus they'll square. You're on The vice squad. It was 20. So we need to find out a solution for the situation as well as we also need to find out whether this equation is parabolic hyperbolic or elliptic. So first of all in the situation we have equals to one B question zero. We don't have anybody and C equals to one. So by this we find out the square minus four A C and b squared minus four is he comes out to be minus four which is less than zero. This implies that if B squared minus four is his less than zero then this situation one is elliptic. So we find out it's elliptic equation. Now this equation this is a special case and the situation is the so called La blast situation. This is boy. The lab class situation. Mhm. On observing the situation, you find that it is a homogeneous leader equation. The slapped a situation is a homogeneous leader equation. The constant coefficient, the quadratic equation, AM scrabble, ISBN plus C equals to zero will be so we put the values of abc from equation one In this quadratic equation and we get a quality vision has and surplus one is equal to see. So the roots but this equation will be one and management. Yeah, it is not equal to zero and the roots of the equation and distinct Therefore we have a solution from Turin number 14.1 of homogeneous linear equations as this U. Is equal to have lifeless I. X plus G. Why minus I. X, r. X, F and G are arbitrary functions of their respective arguments. So that's our answer. Thank you, bob.


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