Making the substitutions to obtain the dv/dt = (18000 - 0.15 v^2)/(3000 - 6t) seems to be high-school algebra, so I leave that part to you.

Using Euler's method in Excel seems pointless, given that the D.E. is separable:

dv/(18000 - 0.15v^2) = dt/(3000 - 6t) =>

(20/3)*dv/(1200000 - v^2) = (1/6)*dt/(500-t).

The expression on the left can be integrated either with a trig substitution or with partial fractions, yielding:

[10/(3*sqrt(1200000)]*ln[(sqrt(1200000) + v)/(sqrt(1200000) - v)] + C = (-1/6)*ln(500 - t) =>

[10/(3*sqrt(1200000)]*ln(1) + C = (-1/6)*ln(500) =>

C = -1.03577 approximately.

Also note that [10/(3*sqrt(1200000)] = 0.0030429 approximately, and if you divide that into the other terms, you have

ln[sqrt(1200000 + v)] - ln[sqrt(1200000) - v] = 340.39 - 54.772*ln(500 - t), or

sqrt(1200000+ v)/sqrt(1200000 - v) = [e^340.39]*(500 - t)^(-54.772).

Now you are in a position to plot the result.

The maximum speed may require some more thought, but it obviously can't exceed 1200000 m/s, considering the square root in the denominator on the left.