mskalsi

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These are questions asked by mskalsi

Dear All

Is it possible to change the position of labels so that they do not overlap with curves of plots? Please see the attached file in which I want to shift label for vertical axes to slightly left and label for horizontal axes to the slightly right.

Plot_Label.mw

Can we overide Maple default dot derivative with 'tau' instead of 't'?

Dear all

I have an operator given below in the image. I want expand this operator upto order 5, when there are three independent variables x, y, t(i=1,2,3). The expansion can also be obtained manually, but that is always prone mistake, is the expansion posible using any routine of Differential Geometry package?

Suppose I have an expression like

Is it possible to reverse the divergence expression using homotopy operator to obtain Psi and Phi?

The above divergence expression is possible since Euler operator of the left side is zero.

I am trying to solve system linear partial differential equations using command "pdsolve". I am surprised to see that the solution given by this command is not satisfying the system, instead, an additional constraint is obtained for an arbitrary function, is there something about "pdsolve" I am missing? 


 

with(PDEtools):

DepVars := [f(x, y, t, u)]

[f(x, y, t, u)]

(1)

Sys := {diff(f(x, y, t, u), u, t)-(diff(f(x, y, t, u), x, y)) = 0, diff(f(x, y, t, u), u, u) = 0, diff(f(x, y, t, u), u, y) = 0, diff(f(x, y, t, u), x, u) = 0, diff(f(x, y, t, u), x, x) = 0, diff(f(x, y, t, u), y, y, y) = 0}

{diff(diff(f(x, y, t, u), t), u)-(diff(diff(f(x, y, t, u), x), y)) = 0, diff(diff(diff(f(x, y, t, u), y), y), y) = 0, diff(diff(f(x, y, t, u), u), u) = 0, diff(diff(f(x, y, t, u), u), x) = 0, diff(diff(f(x, y, t, u), u), y) = 0, diff(diff(f(x, y, t, u), x), x) = 0}

(2)

pdsolve(Sys)

{f(x, y, t, u) = (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t)}

(3)

f := proc (x, y, t, u) options operator, arrow; (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t) end proc

proc (x, y, t, u) options operator, arrow; (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t) end proc

(4)

Sys

{0 = 0, diff(_F3(t), t)-_F3(t) = 0}

(5)

``


 

Download pdsolve_command.mw

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