User doraemonpaul

9 votes

1 answer

577 views

$\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$

laplace-transform contour-integration

asked Jul 11, 2012 at 1:08

8 votes

3 answers

3k views

How to find the general solution of $xy''-(2x+1)y'+x^2y=0$ when we know the general solution of $y''+2y'+xy=0$?

ordinary-differential-equations

asked Nov 28, 2012 at 1:05

8 votes

1 answer

375 views

About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$

indefinite-integrals

asked Apr 6, 2014 at 10:49

6 votes

2 answers

595 views

Why solving $\dfrac{\partial u}{\partial x}=\dfrac{\partial^2u}{\partial y^2}$ like this is wrong?

partial-differential-equations fake-proofs

asked Jul 8, 2012 at 23:08

5 votes

1 answer

241 views

About differentiation under the product integral sign

calculus definite-integrals

asked Aug 1, 2012 at 21:50

5 votes

1 answer

487 views

About fractional differentiation under the integral sign

fractional-calculus

asked Aug 2, 2012 at 23:47

5 votes

0 answers

341 views

How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

partial-differential-equations

asked Dec 28, 2012 at 4:19

5 votes

1 answer

910 views

About finding the general solution of first-order totally nonlinear PDE with two independent variables

partial-differential-equations

asked Mar 29, 2013 at 1:21

4 votes

1 answer

1k views

Is it possible for cosine functions to have Fourier sine series expressions or sine functions to have Fourier cosine series expressions?

fourier-series

asked Nov 29, 2012 at 23:33

3 votes

0 answers

61 views

About the second-order linear ODEs with polynomial coefficients

ordinary-differential-equations

asked Nov 29, 2015 at 19:14

3 votes

0 answers

107 views

fancy about some properties of kernel functions at infinity

analysis definite-integrals integral-transforms

asked Apr 15, 2013 at 4:45

3 votes

3 answers

394 views

Longest cylinder of specified radius in a given cuboid

geometry

asked Aug 4, 2012 at 20:58

3 votes

1 answer

2k views

Does solve PDE by combination of variables always cannot find the general solutions?

partial-differential-equations

asked Aug 18, 2012 at 21:28

2 votes

3 answers

160 views

Iterations of $f(x)=\dfrac{ax+b}{cx+d}$

functional-equations function-and-relation-composition

asked Nov 19, 2012 at 1:53

2 votes

1 answer

666 views

fancy about inverse discrete Fourier sine and cosine transform (i.e. Fourier sine and cosine series)

fourier-analysis integral-transforms

asked Aug 17, 2012 at 2:06

2 votes

1 answer

123 views

Properties about the Generalized Legendre-type polynomial sequence $f_n(x)=\frac{d^n}{dx^n}(p(x)^n)$

analysis ordinary-differential-equations orthogonal-polynomials

asked Aug 12, 2013 at 22:52

2 votes

1 answer

455 views

about discrete versions of "inverse laplace transform"

laplace-transform

asked Dec 3, 2012 at 3:47

2 votes

0 answers

168 views

How to solve the PDEs with more than two independent variables whose their most-general solutions are known?

partial-differential-equations

asked Dec 26, 2012 at 23:48

2 votes

0 answers

807 views

About the inverse laplace transform of sinc function

laplace-transform contour-integration

asked Apr 8, 2013 at 2:33

1 vote

0 answers

73 views

Are there the resources mentioned about finding the general solutions of some first order fully nonlinear PDE examples by method of characteristics?

reference-request partial-differential-equations

asked Jan 24, 2013 at 2:43

1 vote

0 answers

103 views

How are the general skills for complete factorization of arbitrary homogeneous order polynomials in $\mathbb{C}$?

polynomials factoring

asked Dec 28, 2013 at 17:14

1 vote

0 answers

71 views

How the change of variables of a PDE affects the given condition(s)?

partial-differential-equations

asked Mar 12, 2014 at 23:52

1 vote

0 answers

84 views

Properties about the Generalized Hermite-type polynomial sequence $f_n(x)=e^{-p(x)}\frac{d^n}{dx^n}e^{p(x)}$

analysis ordinary-differential-equations orthogonal-polynomials

asked Aug 11, 2013 at 23:21

1 vote

1 answer

390 views

Advanced improper integral involving periodic function of polynomial

calculus real-analysis improper-integrals

asked May 9, 2012 at 0:22

1 vote

1 answer

107 views

How to prove the periodicity of an iterated function?

periodic-functions function-and-relation-composition

asked Nov 20, 2012 at 3:56

1 vote

1 answer

509 views

How to compute the convolution of two functions which diverge at infinity?

convolution

asked Nov 1, 2012 at 19:48

1 vote

0 answers

49 views

About the linear PDE $u_{x_1x_2x_3......x_n}=u$

partial-differential-equations

asked Nov 17, 2017 at 13:01

0 votes

2 answers

146 views

alternative form of the general solution of $u_{xx}+u_{yy}=0$

partial-differential-equations

asked Sep 20, 2012 at 22:19

0 votes

1 answer

181 views

How to determinate the linearly independence between some special functions defined by ODE?

ordinary-differential-equations special-functions

asked May 17, 2012 at 8:27

0 votes

2 answers

215 views

properties about number of solutions of transcendental equations

algebra-precalculus

asked May 30, 2012 at 11:50

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36 Questions

$\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$

How to find the general solution of $xy''-(2x+1)y'+x^2y=0$ when we know the general solution of $y''+2y'+xy=0$?

About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$

Why solving $\dfrac{\partial u}{\partial x}=\dfrac{\partial^2u}{\partial y^2}$ like this is wrong?

About differentiation under the product integral sign

About fractional differentiation under the integral sign

How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

About finding the general solution of first-order totally nonlinear PDE with two independent variables

Is it possible for cosine functions to have Fourier sine series expressions or sine functions to have Fourier cosine series expressions?

About the second-order linear ODEs with polynomial coefficients

fancy about some properties of kernel functions at infinity

Longest cylinder of specified radius in a given cuboid

Does solve PDE by combination of variables always cannot find the general solutions?

Iterations of $f(x)=\dfrac{ax+b}{cx+d}$

fancy about inverse discrete Fourier sine and cosine transform (i.e. Fourier sine and cosine series)

Properties about the Generalized Legendre-type polynomial sequence $f_n(x)=\frac{d^n}{dx^n}(p(x)^n)$

about discrete versions of "inverse laplace transform"

How to solve the PDEs with more than two independent variables whose their most-general solutions are known?

About the inverse laplace transform of sinc function

Are there the resources mentioned about finding the general solutions of some first order fully nonlinear PDE examples by method of characteristics?

How are the general skills for complete factorization of arbitrary homogeneous order polynomials in $\mathbb{C}$?

How the change of variables of a PDE affects the given condition(s)?

Properties about the Generalized Hermite-type polynomial sequence $f_n(x)=e^{-p(x)}\frac{d^n}{dx^n}e^{p(x)}$

Advanced improper integral involving periodic function of polynomial

How to prove the periodicity of an iterated function?

How to compute the convolution of two functions which diverge at infinity?

About the linear PDE $u_{x_1x_2x_3......x_n}=u$

alternative form of the general solution of $u_{xx}+u_{yy}=0$

How to determinate the linearly independence between some special functions defined by ODE?

properties about number of solutions of transcendental equations