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Solve the partial differentialequationUn~C "x +a u=0. 0<r<0 , 1>0 U (x,0)=f (x) (@4) =g(x) 0<1<6 dt {0...

Question

Solve the partial differentialequationUn~C "x +a u=0. 0<r<0 , 1>0 U (x,0)=f (x) (@4) =g(x) 0<1<6 dt {0

Solve the partial differentialequation Un~C "x +a u=0. 0<r<0 , 1>0 U (x,0)=f (x) (@4) =g(x) 0<1<6 dt {0



Answers

Find the indicated partial integral. $$ \int_{0}^{2} \frac{x}{y} d x $$

In the problem we have been given integration fought upon X plus two, it works minus two dx. Now this can be written as a upon X plus two plus be upon x minus two. Hence it is for that equals two in two x minus two plus being two X plus two. Or we have obtained equal to minus one, be equal to one. So integration becomes Diggle minus one upon X plus two plus one upon x minus two dx. So further this is written as minus Ellen mod X plus two plus Ellen mode X minus two plus C. Or this is equal to Ellen mode X minus two upon X plus two plus C. So this is the answer.

The problem we have been given integration minus four upon it's a Squire minus food. This is written as digression, went up on x plus two minus one upon x minus two. The ex no, this is written as Ellen mode X plus two minus Landmark x minus two plus C. This equals two. Ellen mod X plus two upon x minus two plus C. So this is the answer.

Differential equation given to us as partial double derivative, few upon partial derivative of X square plus partial derivative partial second elevator of you upon partial second derivative of y squared is equal to zero. Obviously, if I'm using the word partial so many times. This is the symbol for a partial day elevators. The first thing we need to establish our status. What sort of different equation is this? Now? Clearly since there is already a partial declarative sign, so therefore it implies that the given differential equation is a partial, very big differential equation or derivative equation. So the given differential equation is partial different seal equation. Now, what do we see that? X is the over hill, not just expert. X. And by boat will be be independent variables and you will be the dependent variable. So what can we say that X and Y are the dependent variables whereas you is there independent variable? Now the next thing that we need to establish is the order of the given differential equation. So we know that order of a given differential equation is the highest derivative. Now, since the highest derivative is two. Yeah. So that means that the order of be given differential equation is second order. So it's a second order differential equation. Now the last thing that we need to determine is whether this given differential equations, linear or nonlinear. No. What can we see that there is the both the terms and the given dip are Shal differential equation is actually a second or a derivative, So which means definitely there is no town which has powered one. So therefore what can be said that the given the friendship equation is a non linear differential equation to be a linear differential equation, the highest part of the dependent variable should be one. Since that is not happening in the given differential equations. So that is why it is a nonlinear differential equations. Now let us just summarize what I'll have you seen. So therefore we can state that the given differential equation, since it already has a partial derivative sign is definitely a partial differential equation of second order, and it is a non linear differential equation, since the highest part of the dependent variable is not one. So our final answer is that for the given differential equation it is a partial differential equation of second order and nonlinear in nature.

In problems then we have to music composed. It's disappeared minus three X divided by xq -3. X. Care minus four X. So you're taking ex common board, Numerator and Denominator We Get X into X -3. Do I did buy X into X. Where nine is 3 eggs minus mm So and then yes access because X is not equal to do so we get X minus the divided by eggs. Yeah. No, we find the factors using miller term back down hurt X squared minus. All right. Unless it's my miss for right. It can Also the region SX -3 divided my eggs into extra money. Store Last one You do X minus well. So this will become X money. They divided right? X minus four times X must you were So let It's Nice three divided by X- 94 times X plus one with equal groups, everybody by X minus four. Nice. Really divided by Yes, nice one left on each This version, wow. Now by applying throughout by X man's fall into X plus one regret. X -3 is equal to Hey into S Plus one. Let's be into thanks moments boy. Let's start it. It was improved now to find the radius of air B. First we did X is equal to for new president tools. This is an identity. So four months 3 is one. MS equal groups. Good time last zero. This implies there it is important to run by mm No. So if we put X is equal to four then we get four plus one. He was five times. This implies that is equal to one x 5. Now if you put X these people too -1 is it wasn't too we get in nine years or it's equal to zero minus by Mhm. This implies -5 me. This implies that lee is it will go fall by, right? So the required fashion infections. Uh huh. One by five. Divided by X -4. Less four by five. You're right in my Express. Yeah.


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