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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.