Differential Equations

A projectile was launched from the ground with a certain initial velocity. Militaries used a radar to determine the vertical coordinate y(t) of the projectile for two moments of time t measured in seconds from the moment when the projectile was launched. The radar measurements showed that y(2)=269 meters,y(5)=565 meters. Calculate the maximum of y(t) if it is known as follows:
The projectile was moving along a vertical line.
The acceleration due to gravity g is 9.81 meter/〖second〗^2.
There is a resistance proportional to the velocity of the projectile.
The value of the empirical coefficient ρ is a constant.
Distances are measured in meters.

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    a dy/dt + d^2 y/dt^2 = - 9.81
    try
    y = -(9.81/a) t + [ (V + 9.81/a)/a ] e^-at

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