eq1 := 5*x^4*z^3*y + x^3*y^5*z + 10*exp(x*y*z-2) -98 ;
eq2 := tan(x*y*z-2) + ln(3*x + y + z -7) ;
implicitplot3d({eq1,eq2}, x=0..10, y=0..10, z=0..10, axes=box);
 

So to summarize your problem, you are looking for a particular solution t(x) of the 2nd-order ODE you gave such that c= argmax t(0). 

Is the above a fair summary of your objective? Some questions:

is it always the case that t(-2) = 1 ? In (D(t))(-2) = 2*(c-1)*exp(-(-2)^2)/sqrt(Pi), do you have constraints on your choice of the constant c ?

is the range of x from x=-2 to x=0 ? so that -2 is always your start and 0 always your finish?

Well, for values of c that range between 0 and 10 I always get:

Warning, cannot evaluate the solution further right of -1.6778876, probably a singularity

with the values always close to -1.6.
 

So to summarize your problem, you are looking for a particular solution t(x) of the 2nd-order ODE you gave such that c= argmax t(0). 

Is the above a fair summary of your objective? Some questions:

is it always the case that t(-2) = 1 ? In (D(t))(-2) = 2*(c-1)*exp(-(-2)^2)/sqrt(Pi), do you have constraints on your choice of the constant c ?

is the range of x from x=-2 to x=0 ? so that -2 is always your start and 0 always your finish?

Well, for values of c that range between 0 and 10 I always get:

Warning, cannot evaluate the solution further right of -1.6778876, probably a singularity

with the values always close to -1.6.
 

oops, I see that pagan had already answered your questions

oops, I see that pagan had already answered your questions

> evalf(exp((I*2)*Pi));

                                  1.

> evalf(exp(I*0));

                                  1.

> evalf(exp((I*2)*Pi));

                                  1.

> evalf(exp(I*0));

                                  1.

the triple integral you gave above is equal to a real number, as explained:

int(int(int(y,z=0..5),y=0..5),x=0..9);

                                1125/2

Now a triple integral may arise in a problem involving calculating the volume of a solid, and you can certainly plot3d a solid, perhaps that's what you mean? in this case you need to give more information about your original problem.
 

the triple integral you gave above is equal to a real number, as explained:

int(int(int(y,z=0..5),y=0..5),x=0..9);

                                1125/2

Now a triple integral may arise in a problem involving calculating the volume of a solid, and you can certainly plot3d a solid, perhaps that's what you mean? in this case you need to give more information about your original problem.
 

thumbs can be a delicate symbol too

... in some galaxies

and hot=good

chili=hot is not to be confused with chilly=cold

it looks like x is a dummy variable -- replace it with y and the integral is unchanged.

why don't you put the actual snippet of code, it would be so much easier to see what you're after.

it looks like x is a dummy variable -- replace it with y and the integral is unchanged.

why don't you put the actual snippet of code, it would be so much easier to see what you're after.

cool stuff

cool stuff