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 Apr20 revised Solving inverse Laplace Transform with convolution theroem. added 155 characters in body Apr20 answered The inverse Laplace transform of $s^{3/2}-a-bs \over s^{3/2}+a+bs$ Apr16 answered How to solve the functional equation $f(2x) = (e^x+1)f(x)$? Apr16 revised Second order PDE edited body Apr16 answered Second order PDE Apr16 answered Separation of variables and basis of solutions? Apr16 answered Converting nonlinear second order ODE to first order Apr15 revised Solving inverse Laplace Transform with convolution theroem. added 1 character in body; deleted 1 character in body Apr15 answered Existence and uniqueness for the Cauchy problem for the Laplace equation Apr15 comment Consider the differential equation @falco indeed yes, but the only thing is the solution very difficult to change to the explicit function form of $u$ . Apr14 revised Solving inverse Laplace Transform with convolution theroem. deleted 165 characters in body Apr14 answered Laplace transform nonlinear equation Apr14 answered Consider the differential equation Apr14 answered Necessary and sufficient condition for separation of variables to give all solutions. Apr13 answered Finding a solution to a PDE Apr13 revised Generalized wave equation deleted 8 characters in body Apr12 answered Generalized wave equation Apr12 comment Inverse Laplace transform of $s^{\beta-1}/(s^{\beta}+a)$ The infinte series form you got in fact relates to Fox–Wright function. Apr12 comment Inverse Laplace transform of exponentials and Incomplete gamma functions You still have not getting the real result as $\int_0^\infty\dfrac{x^k}{1+x}dx$ diverges for all non-negative integers $k$ . Apr12 answered Inverse Laplace Transform of $\ln[\frac{s^2+a^2}{s^2+b^2}]$