maple fan

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These are questions asked by maple fan

hello, everyone,
the attached pdf file contain four models, I can't get the solutions of last three models.
help, thank you in advance.

 

123.pdf

The following commands can be plotted by maple 13&15,
but can't be done by 16.

restart;
x1 := sech(sqrt(a)*t); x2 := -sech(sqrt(a)*t)*tanh(sqrt(a)*t);
g1 := proc (t) options operator, arrow; int((int((eval(x2, t = tau))*sin(Omega*tau), tau = 0 .. u))/(eval(x2, t = u))^2, u = 0 .. t) end proc;
plot3d(subs(a = 1, g1(t)), Omega = 0 .. 3, t = 0 .. 1);
g2 := proc (t) options operator, arrow; int((int((eval(x2, t = tau))*cos(Omega*tau), tau = 0 .. u))/(eval(x2, t = u...

> restart;
> F := Int(sqrt((2.138+0.3e-2*exp((4.2^2-z^2)/d^2))^2-2.141^2), z = 0 .. 4.2) = .5;

I have used the fsolve command, it seems like there is a problem.

thank you in advance.

restart;

pde := diff(u(x, y), `$`(x, 2))+4*(diff(u(x, y), `$`(y, 2))) = -x*y;

ibc := {u(0, y) = 0, u(2, y) = 0, u(x, 0) = x*(4-x^2), (D[2](u))(x, 0) = 0};

sol := pdsolve(pde, ibc, numeric);

sol:-plot3d(x = 0 .. 2, y = 0 .. 1, numpoints = 2000, axes = boxed);

 

The final command produce a figure with some sigularity.

how to fix it? I need help, thx you very much.

rsolve(a(n)=2/a(n-1)+1,a(1)=1),

thx in advance.

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