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Solve the following equation with Integrate or DSolve?

Posted 2 months ago
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Hello folks, Think of an equation: -g+Kv=D[v]/D[t] and the conditions are when t=0, v=0; where t is time v is velocity, g is a gravitational acceleration and K is some constant. How do you input these on Mathematica so it could take the integral of the equation and gives result. I already got the result by hand as follows: v=(g(1-e^(k*t))/K). whatever I try I cant get this result. Thanks in advance.

 DSolve[{-g + k* v[t] == D[v[t], t], v[0] == 0}, v[t], t]
 (*  {{v[t] -> -(((-1 + E^(k t)) g)/k)}} *)

or:

 DSolve[{-g + k* v[t] == v'[t], v[0] == 0}, v[t], t]
 (*  {{v[t] -> -(((-1 + E^(k t)) g)/k)}} *)
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