Supersonic ballistics is nonlinear right and not solvable exactly right?

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So I thought I would try to figure out the maximum distance of our 7.62x54 round. obviously I used F=ma and for resistance I used Fdrag=(mass of bullet*density of air*v^2)/ballistic constant. the v^2 terms makes the equation nonlinear and not exactly solvable right? also, the angle at which the force is acting is continually varying, which also adds to the compexity , is this correct? can someone explain some techniques to solve this or what method is used to obtain approximations.

here are the equations i started with

mx''=mPx'^2 where P is a constant from properties of the air and bullet and

my''=mLy'^2-gm where L is the same constant as above, just using sin to get the vertical component of force
i did the standard integrating with respect to t and x after moving over the correct terms, twice to get x and y as functions of t, and the final equations I got were ridiculous.

any insight would be great all
thanks

p.s. sorry about the moronic title to the thread, I rewrote it then forgot to remove a word or two
 
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rcgldr
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