Recent content by Jamp

Thanks... I was thinking about it again on my way to school today and realized that, don't know how I did that... always a good idea to restart from the beginning..:redface: :shy:

What I mean is, take the first function: U(x,y) = (x^0.5)(y^0.5) For any constant, for example 10: 10=(x^0.5)(y^0.5) <=> y=100/x is convex to (0,0). However, 10=(x^2)(y^2) <=> y=sqrt(10-x^2) is concave. These two different functions can not, as far as I can see, have the...

Hello, I am an economics student but this question is purely mathematical. Imagine the function U(x,y)=x^0.5y^0.5 ( sqrt(x) times sqrt(y) ) in space. If we then imagine the same function equal to a constant we get the 2d functions corresponding to the intersections of horizontal planes...

I see. So if I were told that y=x^2 was a solution to the homogeneous eq, then I should try y=x^2z?

Hi! I am looking through some solved exercises. One of them is the following: Solve the equation: x^2 y'' + (x^2 - 3x)y' + (3-x)y = x^4 knowing that y=x is a solution of the homogeneous equation. The professor then solves it by doing the following substitution: y=xz. Then he...

Thank you for your replies. Actually, I'm an economics student. Our mathematics professor explains the concepts very briefly and not very clearly, he focuses more on teaching how to solve specific types of problems that he will put in the exam. However, he usually asks one or two questions...

The point of solving a differential equation is ALWAYS to find the original function that satisfies the equation, is this correct? I'm still having difficulties understanding when that original equation is a one variable, or two variable function. For example: In the case (...)dx + (...)dy =...

Also, for example, sometimes my professor has an equation (...)dx + (...)dy and he substitutes y for something. He then calculates the differential of y like: dy=(...)dx + (...)du and substitutes for the dy in the original equation. Are these two dy's not two different things? I thought the...

Okay, that cleared some doubts.. Now, if y is a function of x, why not have everything as a function of x, just y(x)? Why do we need g(x,y), why not just g(y) since y is already a function of x? Also, if it's all a function of one variable, why can we not just integrate it straight away to get...

Thank you for your effort but there are still some things that do not make sense in my mind about the whole concept. First: With a differential equation of the sort: form dy/dx= g(x,y) or g(x,y)dx+ h(x,y)dy= 0 dy/dx is the derivative of y, right? And the fact that it is not a partial...

Also, something else I don't understand closely related to this ( I know these are very basic abstract conceptual questions that are difficult to explain, so I'm sorry) We usually solve differentials like these: (something in x and y)dx + (something in x and y)dy = Q(x) and we get an...

I know how to solve them, but I don't understand why they are solvable in the first place. The differencial is composed of the partial derivatives of a function, right? From HallsofIvy's post: "There does NOT exist a function "f(x,y)" having those partial derivatives so the equality of mixed...

Ok, I think I almost understand. Your explanation brings up another question though. We learned how to calculate differential equations that are not exact, but if there does not exist a function f(x,y) with those partial derivatives, then how can you calculate it?

But the term in dx (M) is already the first derivative of the function with respect to x. So differentiating M with respect to y is the second derivative d^2f/dxdy . Is this not correct?

Hello! From what I have read, a differential equation is exact if d^2f/dxdy = d^2f/dydx, is this correct? My professor has given us examples of dif. equations that are not exact. However I remember from last semester that Schwartz theorem states that the order in which you differentiate...