The interface variable rtablesize determines what sizes of an Array, Matrix or Vector are shown in detail in the worksheet.  After the command

> interface(rtablesize=infinity):

you would see the whole Matrix.

The interface variable rtablesize determines what sizes of an Array, Matrix or Vector are shown in detail in the worksheet.  After the command

> interface(rtablesize=infinity):

you would see the whole Matrix.

One of the easiest ways to make Maple crash is to iterate a function only slightly more complicated than this one using exact expressions rather than floats.  Just about any function that contains the variable x in more than one place will do.  The iterates rapidly get more and more complicated, eventually using up all available memory.   So, in general, it's much better to insert an evalf into your loop, e.g.

to 20 do
  x := evalf(f(x))
end do:

One of the easiest ways to make Maple crash is to iterate a function only slightly more complicated than this one using exact expressions rather than floats.  Just about any function that contains the variable x in more than one place will do.  The iterates rapidly get more and more complicated, eventually using up all available memory.   So, in general, it's much better to insert an evalf into your loop, e.g.

to 20 do
  x := evalf(f(x))
end do:

Why shouldn't you get a negative value? You should get a positive value when you integrate a positive function over some region. But here the function is positive in some places and negative in others, so there's no reason to expect the result to be positive.

Why shouldn't you get a negative value? You should get a positive value when you integrate a positive function over some region. But here the function is positive in some places and negative in others, so there's no reason to expect the result to be positive.

Euler's integral for the Gamma function is the source of many Laplace transforms.
According to www-history.mcs.st-andrews.ac.uk/Biographies/Euler.html these were studied in Institutiones calculi integralis (1768-70).  You might try
P J Davis, Leonhard Euler's integral : A historical profile of the gamma function, Amer. Math. Monthly 66 (1959), 849-869.

Euler's integral for the Gamma function is the source of many Laplace transforms.
According to www-history.mcs.st-andrews.ac.uk/Biographies/Euler.html these were studied in Institutiones calculi integralis (1768-70).  You might try
P J Davis, Leonhard Euler's integral : A historical profile of the gamma function, Amer. Math. Monthly 66 (1959), 849-869.

Not at all small, but not real: you're taking sin(sqrt(x^2+y^2-t)).  When t > x^2+y^2,
the square root is imaginary, and the sine of an imaginary number is again imaginary: sin(I*t) = I*sinh(t).

Not at all small, but not real: you're taking sin(sqrt(x^2+y^2-t)).  When t > x^2+y^2,
the square root is imaginary, and the sine of an imaginary number is again imaginary: sin(I*t) = I*sinh(t).

> V:= sort(convert(indets(eq1),list), lexorder);

V := [a, b, c, d, e, f, g, h, i, j, k]

The <maple> tag seems not to be working again: that should be

       V := [a, b, c, d, e, f, g, h, i, j, k]

> sort(eq1, ListTools[Reverse](V), tdeg, ascending);

a+k+c*b+e*d+j*i+h*g*f

a + k + c*b + e*d + j*i + h*g*f

> map(sort, %, V);

a+k+b*c+d*e+i*j+f*g*h

a + k + b*c + d*e + i*j + f*g*h

> V:= sort(convert(indets(eq1),list), lexorder);

V := [a, b, c, d, e, f, g, h, i, j, k]

The <maple> tag seems not to be working again: that should be

       V := [a, b, c, d, e, f, g, h, i, j, k]

> sort(eq1, ListTools[Reverse](V), tdeg, ascending);

a+k+c*b+e*d+j*i+h*g*f

a + k + c*b + e*d + j*i + h*g*f

> map(sort, %, V);

a+k+b*c+d*e+i*j+f*g*h

a + k + b*c + d*e + i*j + f*g*h

Maple generally works with complex numbers, not just real numbers.  In terms of the complex numbers, all these are solutions. 

Maple generally works with complex numbers, not just real numbers.  In terms of the complex numbers, all these are solutions. 

For a numerical approximation, use dsolve(..., numeric).  For example:

> S:= dsolve({1/sin(t)*diff(v(t),t)+v(t)=sin(t), v(0)=0}, 
              v(t), numeric);
   plots[odeplot](S, t=0..30, numpoints=300);