Analytically Solving the Magnus Effect with Viscosity in Ball Flight Simulation

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George444fg
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I am trying to add to a problem of mine the viscosity parameter, simulating the fly of a ball. However I obtain the following equations

d^2V_z/dt^2 = WdV_z/dt - dV_x/dt and d^2V_x/dt^2 = WdV_x/dt - dV_z/dt where W is a function linearly dependent to t. Any ideas how I could analytically solve this problem..?
 
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