The main problem is that, Mathematica tries to solve your problem analytically first. So it plugs in symbolic x, and your function can't handle it.
Please refer to this question in http://www.voofie.com/concept/Mathematica/" [Broken]...
Your question really depends on the values of x and y. And your expression doesn't have c. I assumed your function to be:
f(x,y)=\sqrt{a x^8+b x^4y^4+c y^8}
I only outline the method to obtain a power series here.
f(x,y)=c y^8\sqrt{1+\left(\frac{a x^8+b x^4y^4}{c y^8}\right)}
By...
Piano man. Here is a link in http://www.voofie.com/concept/Mathematics/" [Broken] that you maybe interested.
http://www.voofie.com/content/117/an-explicit-formula-for-the-euler-zigzag-numbers-updown-numbers-from-power-series/" [Broken]
I derived the power series of the function sec x +...
Please substitute y = x^2 to your differential equation, and you will find that it is indeed one of the solution.
y = x^2
y' = 2x
y'' = 2
Therefore:
x^2 y'' -3x y' + 4y = 2 x^2 - 6 x^2 + 4x^2 = 0
Actually, you can find a close form for your summation expression. Please refer to http://www.voofie.com/concept/Mathematics/" [Broken] for details:
http://www.voofie.com/content/156/how-to-sum-sinn-q-and-cosn-q/" [Broken]
In short,
\sum _{n=-N}^N \cos (n \theta )=\cos (N \theta )+\cot...
Hello. psholtz. I thought you just do the integration without considering their dependence. It is interesting that x\sqrt{1-y^2} + y\sqrt{1-x^2} = C is a solution. Thank you for your information in the Jacobian as well.
In fact, what you have show is that, x^2 is one of the solution. Since for all other terms other than a_0, they have to be zero in order for the expression to equal to zero.
I am sorry, but your 2nd equation:
\sqrt{1-y^2}dx + \sqrt{1-x^2}dy = 0
cannot be integrated to get the 3rd equation:
x\sqrt{1-y^2} + y\sqrt{1-x^2} = C
You cannot integrate term by term, from dx to x, since \sqrt{1-y^2} depends on x, and \sqrt{1-x^2} depends on y.
In fact, if you...
Hello. Please refer to my article in http://www.voofie.com/concept/Mathematics/" [Broken]:
http://www.voofie.com/content/18/solving-system-of-first-order-linear-differential-equations-with-matrix-exponential-method/" [Broken]
What you really need is matrix exponential, instead of matrix...
For your first equation, please refer to this question in http://www.voofie.com/concept/Mathematics/" [Broken]:
http://www.voofie.com/content/152/how-to-prove-eat-e-at_0-eat-t_0/" [Broken]
I think you typed wrong in this formula:
exp(At)_t=0 = I
0 is not equal to I. And your what's your...
Hello ferry2, I have solved your 2nd equation here:
http://www.voofie.com/content/146/how-to-solve-2x12-y--2-2x1-y-4-y-0/" [Broken]
And the solution is given by:
y(x) = C_1(2x+1) +C_2 (2x+1) \ln (2x+1)
Generating Function of your number
soroush1358, I have answer your question in this post: http://www.voofie.com/content/144/sum-of-subsets-with-k-elements-having-a-total-sum-of-r/" [Broken].
You can read more Mathematics related articles in http://www.voofie.com/concept/Mathematics/"...