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Aug
22
asked solution of $y' + y^2 = \varphi^2(x)$
Aug
19
asked Solving second order differential equation numerically with values given at intermediate points.
Aug
19
accepted Proof of definite integral is finite
Aug
19
accepted function with zero first to n'th derivative at end points
Aug
19
comment Solution of $y''(x) -k = \delta(x-x_0)y(x)$
yes, I understood this when I carefully read the boundary conditions. Thanks again for the explanation.
Aug
19
comment Solution of $y''(x) -k = \delta(x-x_0)y(x)$
@Dmoreno, After what you have derived we assume $u_y =0$(i.e. there is no flow in the direction perpendicular to gravity which follows by symmetry) and arrive at equation in the question. While solving Usual NS equations we specify value of velocity at the boundary. Here friction force is added to make sure velocity in the vicinity of wall be made gradually zero. Velocity profile can be then expected to be not parabolic nearby wall.
Aug
19
accepted Solution of $y''(x) -k = \delta(x-x_0)y(x)$
Aug
19
comment Solution of $y''(x) -k = \delta(x-x_0)y(x)$
@Winter, Thanks a lot for the answer..!!
Aug
19
comment Solution of $y''(x) -k = \delta(x-x_0)y(x)$
@Dmoreno, I have added the physical background.
Aug
19
revised Solution of $y''(x) -k = \delta(x-x_0)y(x)$
added 448 characters in body; edited title
Aug
19
comment Solution of $y''(x) -k = \delta(x-x_0)y(x)$
@hjpotter92, there is difference in the right hand side of the two questions.
Aug
19
comment second order differential equation with Green's function
@Dmoreno, I think I need your expertise in here math.stackexchange.com/questions/902934/…
Aug
19
asked Solution of $y''(x) -k = \delta(x-x_0)y(x)$
Aug
19
comment second order differential equation with Green's function
@Silynn, I think I have arrived at solution following your comment. If you can make it as answer I can mark it as the correct one.
Aug
19
revised second order differential equation with Green's function
added 268 characters in body
Aug
19
comment second order differential equation with Green's function
@Silynn, yes I tried that one. Heaviside step function's differentiation gives delta function. But do not know integration of Heaviside function.
Aug
19
asked second order differential equation with Green's function
Jul
2
awarded  Curious
Nov
27
asked Proof of definite integral is finite
Nov
18
answered function with zero first to n'th derivative at end points