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Sep
18
revised How to prove $(x^2-1) \frac{d}{dx}(x \frac{dE(x)}{dx})=xE(x)$
added 664 characters in body
Sep
18
revised How to prove $(x^2-1) \frac{d}{dx}(x \frac{dE(x)}{dx})=xE(x)$
added 64 characters in body
Sep
18
revised How to prove $(x^2-1) \frac{d}{dx}(x \frac{dE(x)}{dx})=xE(x)$
added 1 characters in body
Sep
18
asked How to prove $(x^2-1) \frac{d}{dx}(x \frac{dE(x)}{dx})=xE(x)$
Sep
14
accepted Second order non-linear differential equation
Sep
14
accepted To find the closed form of $ f^{-1}(x)$ if $3f(x)=e^{x}+e^{\alpha x}+e^{\alpha^2 x}$
Sep
14
accepted What is the shortest path equation between 2 points on a cone?
Sep
14
answered Length of chord DE
Sep
14
comment How to solve the partial differential equation $a\frac {\partial L}{\partial a}+b\frac {\partial L}{\partial b}= L $
(+1) Thanks for help to show $\int\cos^{2n}t~dt$.
Sep
14
comment How to solve the partial differential equation $a\frac {\partial L}{\partial a}+b\frac {\partial L}{\partial b}= L $
@LVK: Thanks for advice. You are right but to rediscover some relations gives me deep understanding. It is just self-learning method. I am trying to learn to catch fish not to wait for a ready one in my stomach. Thank you for your understanding and links. I have been checking them.
Sep
14
comment How to solve the partial differential equation $a\frac {\partial L}{\partial a}+b\frac {\partial L}{\partial b}= L $
@doraemonpaul: I have been self-studying on elliptic integrals. I like to try different approach to a problem. I am not so much experienced about some subjects such as PDEs. Actually I knew binom method but I tried to find a solution via a different way . Maybe I have lost myself in big PDE Ocean. Thanks for answer.
Sep
13
asked How to solve the partial differential equation $a\frac {\partial L}{\partial a}+b\frac {\partial L}{\partial b}= L $
Sep
13
comment The integral relation between Perimeter of ellipse and Quarter of Perimeter
@joriki: Thank you very much for your answer. It is OK and clear. I know what average means. if I draw the function , I can see geometrically the periodic function relations. I just asked to see the relation proof via analytic way such as variable changing . It was for me a challenge to solve such relation. Thanks a lot for answer again.
Sep
13
answered The integral relation between Perimeter of ellipse and Quarter of Perimeter
Sep
12
comment How can I express such function as known functions or power series?
thanks for answer. Can we find $\lim x-->\infty$ $f(x)$? Any suggestion?
Sep
12
accepted Surface of Cone
Sep
12
comment The integral relation between Perimeter of ellipse and Quarter of Perimeter
@SeanEberhard: I proved it via geometric relation. I wonder how to show it via some analytic methods in relation 2. Thanks
Sep
12
revised The integral relation between Perimeter of ellipse and Quarter of Perimeter
added 14 characters in body
Sep
12
asked The integral relation between Perimeter of ellipse and Quarter of Perimeter
Sep
11
comment How can I express such function as known functions or power series?
@MichaelHardy : Really it is so. Thanks a lot for format change.