Recent content by Chromosom

Yeah, it does. Thanks for your answer. I started to calculate it and I got it. For future visitors: you must multiplicate first equation by \cos x and second by \sin x and try to reduce it.

Homework Statement y^{\prime\prime}+y=\frac{1}{\sin x} Homework Equations The Attempt at a Solution I solved the homogenous equation: y=C_1\sin x+C_2\cos x, and then I tried to use method of variable the constant. But the equation system is rather hard. Do you know any other...

Very clever :) y^\prime=y^\prime+xy^{\prime\prime}-2y^\prime y^{\prime\prime} xy^{\prime\prime}-2y^\prime y^{\prime\prime}=0 y^{\prime\prime}\left(x-2y^\prime\right)=0 Now we could expect that y=ax+b, but: y^\prime=a ax+b=ax-a^2 b+a^2=0 The last equation must be satisfied in order to be...

Homework Statement y=xy^\prime-\left(y^\prime\right)^2 Homework Equations The Attempt at a Solution Unfortunately, I do not have any good idea. I tried y=xt(x), but the equation only became worse.

Homework Statement f:\ v(x,y)=4xy+2x The task is to calculate the imaginary part. Homework Equations The Attempt at a Solution I have no idea what to do because in my opinion u(x,y) can be anything. For example: f(x,y)=4xy+2x+(3x-4y)\text i. But I must be wrong. I would...

Homework Statement Find example of function that saatisfies ##\lim\limits_{(x,y)\to(0,0)}f(x,y)=0## and ##0\neq\lim\limits_{x\to y}\lim\limits_{y\to0}f(x,y)\neq\lim\limits_{y\to0}\lim\limits_{x\to0}f(x,y)## The Attempt at a Solution In my opinion it is impossible. Let...

Homework Statement Prove that function has directional derivative in every direction, but is not differentiable in (0,0): f(x,y)=\begin{cases}\frac{x^3}{x^2+y^2},&(x,y)\neq(0,0)\\ \\0,&(x,y)=(0,0)\end{cases} The Attempt at a Solution I have already proved that it has directional...

I am looking for an exact value of absorption coefficient of aluminium for microwaves, but I can not find it in the internet. Anyone knows where I can find it?

Thanks for help:) but then I have \sqrt{1+\cosh^2x} and nothing to do with it...

Yeah. x\in[0,b] Thanks for help :)

It's other language... in translation, I need to compute y coordinate of mass center.

The original problem was: calculate y coordinate of mass center of line: y=\text{arsinh}\,\frac xa I need to compute: y_a=\frac{\int_Ly\,\text dl}{\int_L\text dl} and I got this integral from first post. Any other method for mass center? Thanks for answers by the way :)

Homework Statement Integral: \int\sqrt{1+\frac{1}{a^2+x^2}}\,\text dx Homework Equations The Attempt at a Solution I don't know any method at the moment. Maybe Euler substitution? But this integral is \int\sqrt{\frac{1+a^2+x^2}{a^2+x^2}} after making some calculation, but it...

Homework Statement I have got a question concerning the following function: f(x,y)=\log\left(x^2+y^2\right) Partial derivatives are: \frac{\partial^2f}{\partial x^2}=\frac{y^2-x^2}{\left(x^2+y^2\right)^2} and \frac{\partial^2f}{\partial y^2}=\frac{x^2-y^2}{\left(x^2+y^2\right)^2} The...